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29519750 | 10.1007/s00023-016-0469-6 | We describe general constraints on the elliptic genus of a 2d supersymmetric
conformal field theory which has a gravity dual with large radius in Planck
units. We give examples of theories which do and do not satisfy the bounds we
derive, by describing the elliptic genera of symmetric product orbifolds of
$K3$, product manifolds, certain simple families of Calabi-Yau hypersurfaces,
and symmetric products of the "Monster CFT." We discuss the distinction between
theories with supergravity duals and those whose duals have strings at the
scale set by the AdS curvature. Under natural assumptions we attempt to
quantify the fraction of (2,2) supersymmetric conformal theories which admit a
weakly curved gravity description, at large central charge.Comment: 50 pages, 9 figures, v2: minor corrections to section | Elliptic Genera and 3d Gravity | elliptic genera and 3d gravity | elliptic genus supersymmetric conformal planck units. satisfy bounds derive describing elliptic genera orbifolds manifolds families calabi hypersurfaces monster cft. distinction supergravity duals duals strings curvature. assumptions attempt quantify supersymmetric conformal admit weakly curved pages minor | non_dup | [] |
29546337 | 10.1007/s00023-016-0470-0 | We consider the stationary incompressible Navier-Stokes equation in the
half-plane with inhomogeneous boundary condition. We prove existence of strong
solutions for boundary data close to any Jeffery-Hamel solution with small flux
evaluated on the boundary. The perturbation of the Jeffery-Hamel solution on
the boundary has to satisfy a nonlinear compatibility condition which
corresponds to the integral of the velocity field on the boundary. The first
component of this integral is the flux which is an invariant quantity, but the
second, called the asymmetry, is not invariant, which leads to one
compatibility condition. Finally, we prove existence of weak solutions, as well
as weak-strong uniqueness for small data.Comment: 28 pages, 4 figure | On the stationary Navier-Stokes equations in the half-plane | on the stationary navier-stokes equations in the half-plane | stationary incompressible navier stokes inhomogeneous condition. jeffery hamel boundary. perturbation jeffery hamel satisfy compatibility boundary. quantity asymmetry compatibility condition. uniqueness pages | non_dup | [] |
29534751 | 10.1007/s00023-016-0471-z | The quantization of mirror curves to toric Calabi--Yau threefolds leads to
trace class operators, and it has been conjectured that the spectral properties
of these operators provide a non-perturbative realization of topological string
theory on these backgrounds. In this paper, we find an explicit form for the
integral kernel of the trace class operator in the case of local P1xP1, in
terms of Faddeev's quantum dilogarithm. The matrix model associated to this
integral kernel is an O(2) model, which generalizes the ABJ(M) matrix model. We
find its exact planar limit, and we provide detailed evidence that its 1/N
expansion captures the all genus topological string free energy on local P1xP1.Comment: 37 pages, 4 figures; v2: misprints corrected, comments and Appendix
adde | Matrix models from operators and topological strings, 2 | matrix models from operators and topological strings, 2 | quantization mirror toric calabi threefolds trace conjectured perturbative realization topological backgrounds. kernel trace faddeev dilogarithm. kernel generalizes model. planar captures genus topological pages misprints corrected comments adde | non_dup | [] |
29541575 | 10.1007/s00023-016-0472-y | We study vacuum polarisation effects of a Dirac field coupled to an external
scalar field and derive a semi-classical expansion of the regu-larised vacuum
energy. The leading order of this expansion is given by a classical formula due
to Chin, Lee-Wick and Walecka, for which our result provides the first rigorous
proof. We then discuss applications to the non-relativistic large-coupling
limit of an interacting system, and to the stability of homogeneous systems.Comment: Revised version to appear in AHP (DOI: 10.1007/s00023-016-0472-y | Semi-classical Dirac vacuum polarisation in a scalar field | semi-classical dirac vacuum polarisation in a scalar field | polarisation dirac derive regu larised energy. chin wick walecka rigorous proof. relativistic interacting homogeneous revised | non_dup | [] |
29531447 | 10.1007/s00023-016-0473-x | This paper consists of three parts. In part I, we microscopically derive
Ginzburg--Landau (GL) theory from BCS theory for translation-invariant systems
in which multiple types of superconductivity may coexist. Our motivation are
unconventional superconductors. We allow the ground state of the effective gap
operator $K_{T_c}+V$ to be $n$-fold degenerate and the resulting GL theory then
couples $n$ order parameters. In part II, we study examples of multi-component
GL theories which arise from an isotropic BCS theory. We study the cases of (a)
pure $d$-wave order parameters and (b) mixed $(s+d)$-wave order parameters, in
two and three dimensions. In part III, we present explicit choices of
spherically symmetric interactions $V$ which produce the examples in part II.
In fact, we find interactions $V$ which produce ground state sectors of
$K_{T_c}+V$ of arbitrary angular momentum, for open sets of of parameter
values. This is in stark contrast with Schr\"odinger operators $-\nabla^2+V$,
for which the ground state is always non-degenerate. Along the way, we prove
the following fact about Bessel functions: At its first maximum, a half-integer
Bessel function is strictly larger than all other half-integer Bessel
functions.Comment: 57 pages, 2 tables and 1 figure. Final version to appear in Ann. H.
Poincar\' | Multi-component Ginzburg-Landau theory: microscopic derivation and
examples | multi-component ginzburg-landau theory: microscopic derivation and examples | parts. microscopically derive ginzburg landau translation superconductivity coexist. motivation unconventional superconductors. degenerate couples parameters. arise isotropic theory. dimensions. choices spherically sectors values. stark schr odinger nabla degenerate. bessel integer bessel strictly integer bessel pages tables figure. ann. poincar | non_dup | [] |
29538527 | 10.1007/s00023-016-0478-5 | We consider the strong field asymptotics for the occurrence of zero modes of
certain Weyl-Dirac operators on $\mathbb{R}^3$. In particular we are interested
in those operators $\mathcal{D}_{B}$ for which the associated magnetic field
$B$ is given by pulling back a $2$-form $\beta$ from the sphere $\mathbb{S}^2$
to $\mathbb{R}^3$ using a combination of the Hopf fibration and inverse
stereographic projection. If $\int_{\mathbb{S}^2}\beta\neq0$ we show that \[
\sum_{0\le t\le T}\mathrm{dim}\,\mathrm{Ker}\,\mathcal{D}_{tB}
=\frac{T^2}{8\pi^2}\,\biggl\lvert\int_{\mathbb{S}^2}\beta\biggr\rvert\,\int_{\mathbb{S}^2}\lvert{\beta}\rvert+o(T^2)
\] as $T\to+\infty$. The result relies on Erd\H{o}s and Solovej's
characterisation of the spectrum of $\mathcal{D}_{tB}$ in terms of a family of
Dirac operators on $\mathbb{S}^2$, together with information about the strong
field localisation of the Aharonov-Casher zero modes of the latter.Comment: 24 pages, typos corrected, some minor rewordin | Asymptotics for Erdos-Solovej Zero Modes in Strong Fields | asymptotics for erdos-solovej zero modes in strong fields | asymptotics occurrence weyl dirac mathbb interested mathcal pulling beta sphere mathbb mathbb hopf fibration stereographic projection. mathbb beta mathrm mathrm mathcal frac biggl lvert mathbb beta biggr rvert mathbb lvert beta rvert infty relies solovej characterisation mathcal dirac mathbb localisation aharonov casher pages typos corrected minor rewordin | non_dup | [] |
25017068 | 10.1007/s00023-016-0481-x | De Rham cohomology with spacelike compact and timelike compact supports has
recently been noticed to be of importance for understanding the structure of
classical and quantum Maxwell theory on curved spacetimes. Similarly causally
restricted cohomologies of different differential complexes play a similar role
in other gauge theories. We introduce a method for computing these causally
restricted cohomologies in terms of cohomologies with either compact or
unrestricted supports. The calculation exploits the fact that the de
Rham-d'Alembert wave operator can be extended to a chain map that is homotopic
to zero and that its causal Green function fits into a convenient exact
sequence. As a first application, we use the method on the de Rham complex,
then also on the Calabi (or Killing-Riemann-Bianchi) complex, which appears in
linearized gravity on constant curvature backgrounds. We also discuss
applications to other complexes, as well as generalized causal structures and
functoriality.Comment: 26 pages, no figures, BibTeX; v2: some sections rearranged, slightly
modified notation; close to published versio | Cohomology with causally restricted supports | cohomology with causally restricted supports | rham cohomology spacelike timelike supports noticed maxwell curved spacetimes. causally restricted cohomologies complexes theories. causally restricted cohomologies cohomologies unrestricted supports. exploits rham alembert homotopic causal fits convenient sequence. rham calabi killing riemann bianchi linearized curvature backgrounds. complexes causal pages bibtex rearranged notation versio | non_dup | [] |
42644255 | 10.1007/s00023-016-0487-4 | We consider a system of $N$ bosons confined to a thin waveguide, i.e.\ to a
region of space within an $\varepsilon$-tube around a curve in $\mathbb{R}^3$.
We show that when taking simultaneously the NLS limit $N\to \infty$ and the
limit of strong confinement $\varepsilon\to 0$, the time-evolution of such a
system starting in a state close to a Bose-Einstein condensate is approximately
captured by a non-linear Schr\"odinger equation in one dimension. The strength
of the non-linearity in this Gross-Pitaevskii type equation depends on the
shape of the cross-section of the waveguide, while the "bending" and the
"twisting" of the waveguide contribute potential terms. Our analysis is based
on an approach to mean-field limits developed by Pickl.Comment: Final version to appear in Annales Henri Poincar | The NLS limit for bosons in a quantum waveguide | the nls limit for bosons in a quantum waveguide | bosons confined waveguide i.e. varepsilon tube mathbb simultaneously infty confinement varepsilon bose einstein condensate captured schr odinger dimension. linearity gross pitaevskii waveguide bending twisting waveguide terms. annales henri poincar | non_dup | [] |
29548115 | 10.1007/s00023-016-0489-2 | We give a constructive proof for the existence of an $N$-dimensional Bloch
basis which is both smooth (real analytic) and periodic with respect to its
$d$-dimensional quasi-momenta, when $1\leq d\leq 2$ and $N\geq 1$. The
constructed Bloch basis is conjugation symmetric when the underlying projection
has this symmetry, hence the corresponding exponentially localized composite
Wannier functions are real. In the second part of the paper we show that by
adding a weak, globally bounded but not necessarily constant magnetic field,
the existence of a localized basis is preserved.Comment: 32 pages, to appear in Annales Henri Poincar | On the construction of composite Wannier functions | on the construction of composite wannier functions | constructive bloch analytic quasi momenta bloch conjugation projection exponentially localized composite wannier real. adding globally necessarily localized pages annales henri poincar | non_dup | [] |
29554538 | 10.1007/s00023-016-0496-3 | Given a family of self-adjoint operators $(A_t)_{t\in T}$ indexed by a
parameter $t$ in some topological space $T$, necessary and sufficient
conditions are given for the spectrum $\sigma(A_t)$ to be Vietoris continuous
with respect to $t$. Equivalently the boundaries and the gap edges are
continuous in $t$. If $(T,d)$ is a complete metric space with metric $d$, these
conditions are extended to guarantee H\"older continuity of the spectral
boundaries and of the spectral gap edges. As a corollary, an upper bound is
provided for the size of closing gaps.Comment: 15 pages, 1 figur | Continuity of the spectrum of a field of self-adjoint operators | continuity of the spectrum of a field of self-adjoint operators | adjoint indexed topological sigma vietoris equivalently boundaries guarantee older continuity boundaries edges. corollary closing pages figur | non_dup | [] |
29538534 | 10.1007/s00023-016-0497-2 | We study the asymptotic distribution of the resonances near the Landau levels
$\Lambda\_q =(2q+1)b$, $q \in \mathbb{N}$, of the Dirichlet (resp. Neumann,
resp. Robin) realization in the exterior of a compact domain of $\mathbb{R}^3$
of the 3D Schr{\"o}dinger operator with constant magnetic field of scalar
intensity $b\textgreater{}0$. We investigate the corresponding resonance
counting function and obtain the main asymptotic term. In particular, we prove
the accumulation of resonances at the Landau levels and the existence of
resonance free sectors. In some cases, it provides the discreteness of the set
of embedded eigenvalues near the Landau levels | Counting function of magnetic resonances for exterior problems | counting function of magnetic resonances for exterior problems | asymptotic resonances landau lambda mathbb dirichlet resp. neumann resp. robin realization exterior mathbb schr dinger textgreater counting asymptotic term. accumulation resonances landau sectors. discreteness embedded eigenvalues landau | non_dup | [] |
29570711 | 10.1007/s00023-016-0513-6 | We consider the many body quantum dynamics of systems of bosons interacting
through a two-body potential $N^{3\beta-1} V (N^\beta x)$, scaling with the
number of particles $N$. For $0< \beta < 1$, we obtain a norm-approximation of
the evolution of an appropriate class of data on the Fock space. To this end,
we need to correct the evolution of the condensate described by the
one-particle nonlinear Schr\"odinger equation by means of a fluctuation
dynamics, governed by a quadratic generator.Comment: 78 pages, acknowledgements adde | Quantum many-body fluctuations around nonlinear Schr\"odinger dynamics | quantum many-body fluctuations around nonlinear schr\"odinger dynamics | bosons interacting beta beta beta norm fock space. condensate schr odinger fluctuation governed quadratic pages acknowledgements adde | non_dup | [] |
42676320 | 10.1007/s00023-016-0515-4 | We construct candidates for observables in wedge-shaped regions for a class
of 1+1-dimensional integrable quantum field theories with bound states whose
S-matrix is diagonal, by extending our previous methods for scalar S-matrices.
Examples include the Z(N)-Ising models, the A_N-affine Toda field theories and
some S-matrices with CDD factors.
We show that these candidate operators which are associated with elementary
particles commute weakly on a dense domain. For the models with two species of
particles, we can take a larger domain of weak commutativity and give an
argument for the Reeh-Schlieder property.Comment: minor corrections, as to appear in Ann H Poincare; 46 pages, 2 tikz
figure | Wedge-local fields in integrable models with bound states II. Diagonal
S-matrix | wedge-local fields in integrable models with bound states ii. diagonal s-matrix | candidates observables wedge shaped integrable diagonal extending matrices. ising affine toda factors. candidate elementary commute weakly dense domain. commutativity argument reeh schlieder minor poincare pages tikz | non_dup | [] |
42705580 | 10.1007/s00023-016-0520-7 | The paper is devoted to operators given formally by the expression
\begin{equation*} -\partial_x^2+\big(\alpha-\frac14\big)x^{-2}. \end{equation*}
This expression is homogeneous of degree minus 2. However, when we try to
realize it as a self-adjoint operator for real $\alpha$, or closed operator for
complex $\alpha$, we find that this homogeneity can be broken.
This leads to a definition of two holomorphic families of closed operators on
$L^2({\mathbb R}_+)$, which we denote $H_{m,\kappa}$ and $H_0^\nu$, with
$m^2=\alpha$, $-1<\Re(m)<1$, and where $\kappa,\nu\in{\mathbb C}\cup\{\infty\}$
specify the boundary condition at $0$. We study these operators using their
explicit solvability in terms of Bessel-type functions and the Gamma function.
In particular, we show that their point spectrum has a curious shape: a string
of eigenvalues on a piece of a spiral. Their continuous spectrum is always
$[0,\infty[$. Restricted to their continuous spectrum, we diagonalize these
operators using a generalization of the Hankel transformation. We also study
their scattering theory.
These operators are usually non-self-adjoint. Nevertheless, it is possible to
use concepts typical for the self-adjoint case to study them. Let us also
stress that $-1<\Re(m)<1$ is the maximal region of parameters for which the
operators $H_{m,\kappa}$ can be defined within the framework of the Hilbert
space $L^2({\mathbb R}_+)$.Comment: The title has been changed, the previous one was : On almost
homogeneous Schroedinger operator | On Schroedinger operators with inverse square potentials on the
half-line | on schroedinger operators with inverse square potentials on the half-line | devoted formally begin alpha frac homogeneous minus realize adjoint alpha alpha homogeneity broken. holomorphic families mathbb kappa alpha kappa mathbb infty specify solvability bessel gamma function. curious eigenvalues piece spiral. infty restricted diagonalize generalization hankel transformation. theory. adjoint. nevertheless concepts adjoint them. maximal kappa hilbert mathbb .comment title changed homogeneous schroedinger | non_dup | [] |
29509602 | 10.1007/s00023-016-0521-6 | The Principle of Perturbative Agreement, as introduced by Hollands & Wald, is
a renormalisation condition in quantum field theory on curved spacetimes. This
principle states that the perturbative and exact constructions of a field
theoretic model given by the sum of a free and an exactly tractable interaction
Lagrangean should agree. We develop a proof of the validity of this principle
in the case of scalar fields and quadratic interactions without derivatives
which differs in strategy from the one given by Hollands & Wald for the case of
quadratic interactions encoding a change of metric. Thereby we profit from the
observation that, in the case of quadratic interactions, the composition of the
inverse classical M{\o}ller map and the quantum M{\o}ller map is a contraction
exponential of a particular type. Afterwards, we prove a generalisation of the
Principle of Perturbative Agreement and show that considering an arbitrary
quadratic contribution of a general interaction either as part of the free
theory or as part of the perturbation gives equivalent results. Motivated by
the thermal mass idea, we use our findings in order to extend the construction
of massive interacting thermal equilibrium states in Minkowski spacetime
developed by Fredenhagen & Lindner to the massless case. In passing, we also
prove a property of the construction of Fredenhagen & Lindner which was
conjectured by these authors.Comment: 57 pages; alternative PPA proof in Sec. 3.4 revised and given only
for non-derivative perturbations; added Appendices C and D to substantiate
certain statements in Sec. 5; v3: minor improvements in Lemma 3.2 & D.1,
added Remark 5. | The generalised principle of perturbative agreement and the thermal mass | the generalised principle of perturbative agreement and the thermal mass | perturbative hollands wald renormalisation curved spacetimes. perturbative constructions theoretic tractable lagrangean agree. validity quadratic derivatives differs hollands wald quadratic encoding metric. thereby profit quadratic ller ller contraction exponential type. afterwards generalisation perturbative quadratic perturbation results. motivated extend massive interacting minkowski spacetime fredenhagen lindner massless case. passing fredenhagen lindner conjectured pages sec. revised perturbations appendices substantiate statements sec. minor improvements remark | non_dup | [] |
29541776 | 10.1007/s00023-016-0523-4 | We extend Poincar\'e's theory of orientation-preserving homeomorphisms from
the circle to circloids with decomposable boundary. As special cases, this
includes both decomposable cofrontiers and decomposable cobasin boundaries.
More precisely, we show that if the rotation number on an invariant circloid
$A$ of a surface homeomorphism is irrational and the boundary of $A$ is
decomposable, then the dynamics are monotonically semiconjugate to the
respective irrational rotation. This complements classical results by Barge and
Gillette on the equivalence between rational rotation numbers and the existence
of periodic orbits and yields a direct analogue to the Poincar\'e
Classification Theorem for circle homeomorphisms. Moreover, we show that the
semiconjugacy can be obtained as the composition of a monotone circle map with
a `universal factor map', only depending on the topological structure of the
circloid. This implies, in particular, that the monotone semiconjugacy is
unique up to post-composition with a rotation. If, in addition, $A$ is a
minimal set, then the semiconjugacy is almost one-to-one if and only if there
exists a biaccessible point. In this case, the dynamics on $A$ are almost
automorphic. Conversely, we use the Anosov-Katok method to build a
$C^\infty$-example where all fibres of the semiconjugacy are non-trivial.Comment: 20 pages, 2 figures. Updated version addressing comments by the
refere | Poincar\'e theory for decomposable cofrontiers | poincar\'e theory for decomposable cofrontiers | extend poincar preserving homeomorphisms circle circloids decomposable boundary. decomposable cofrontiers decomposable cobasin boundaries. precisely circloid homeomorphism irrational decomposable monotonically semiconjugate respective irrational rotation. complements barge gillette equivalence rational orbits analogue poincar circle homeomorphisms. semiconjugacy monotone circle universal topological circloid. monotone semiconjugacy rotation. semiconjugacy biaccessible point. automorphic. conversely anosov katok build infty fibres semiconjugacy pages figures. updated addressing comments refere | non_dup | [] |
77415347 | 10.1007/s00023-016-0524-3 | We introduce and study a Markov field on the edges of a graph $\mathcal{G}$ in dimension $\textit{d}$ ≥ 2 whose configurations are spin networks. The field arises naturally as the edge-occupation field of a Poissonian model (a soup) of non-backtracking loops and walks characterized by a spatial Markov property such that, conditionally on the value of the edge-occupation field on a boundary set that splits the graph into two parts, the distributions of the loops and arcs contained in the two parts are independent of each other. The field has a Gibbs distribution with a Hamiltonian given by a sum of terms which involve only edges incident on the same vertex. Its free energy density and other quantities can be computed exactly, and their critical behavior analyzed, in any dimension.The first author acknowledges the support of Vidi Grant 639.032.916 of the Netherlands Organization for Scientific Research (NWO). The second author was partially supported by the Knut and Alice Wallenberg Foundation.This is the final version of the article. It first appeared from Springer via https://doi.org/10.1007/s00023-016-0524- | Non-Backtracking Loop Soups and Statistical Mechanics on Spin Networks | non-backtracking loop soups and statistical mechanics on spin networks | markov mathcal textit configurations networks. arises naturally occupation poissonian soup backtracking loops walks markov conditionally occupation splits loops arcs other. gibbs involve incident vertex. quantities dimension.the acknowledges vidi netherlands partially knut alice wallenberg foundation.this article. appeared springer | non_dup | [] |
42675661 | 10.1007/s00023-016-0532-3 | The main objective of this paper is to systematically develop a spectral and
scattering theory for selfadjoint Schr\"odinger operators with
$\delta$-interactions supported on closed curves in $\mathbb R^3$. We provide
bounds for the number of negative eigenvalues depending on the geometry of the
curve, prove an isoperimetric inequality for the principal eigenvalue, derive
Schatten--von Neumann properties for the resolvent difference with the free
Laplacian, and establish an explicit representation for the scattering matrix.Comment: to appear in Annales Henri Poincar | Spectral theory for Schr\"odinger operators with $\delta$-interactions
supported on curves in $\mathbb R^3$ | spectral theory for schr\"odinger operators with $\delta$-interactions supported on curves in $\mathbb r^3$ | systematically selfadjoint schr odinger delta mathbb bounds eigenvalues isoperimetric inequality principal eigenvalue derive schatten neumann resolvent laplacian establish annales henri poincar | non_dup | [] |
42678187 | 10.1007/s00023-016-0533-2 | We develop an approach to construct Poisson algebras for non-linear scalar
field theories that is based on the Cahiers topos model for synthetic
differential geometry. In this framework the solution space of the field
equation carries a natural smooth structure and, following Zuckerman's ideas,
we can endow it with a presymplectic current. We formulate the Hamiltonian
vector field equation in this setting and show that it selects a family of
observables which forms a Poisson algebra. Our approach provides a clean
splitting between geometric and algebraic aspects of the construction of a
Poisson algebra, which are sufficient to guarantee existence, and analytical
aspects that are crucial to analyze its properties.Comment: v2: 24 pages; compatible with version to appear in Annales Henri
Poincar | Poisson algebras for non-linear field theories in the Cahiers topos | poisson algebras for non-linear field theories in the cahiers topos | poisson algebras cahiers topos synthetic geometry. carries zuckerman ideas endow presymplectic current. formulate selects observables poisson algebra. clean splitting geometric algebraic poisson guarantee crucial analyze pages compatible annales henri poincar | non_dup | [] |
42742142 | 10.1007/s00023-016-0534-1 | Let $H=-\Delta+V$ be a Schr\"odinger operator on $L^2(\mathbb R^4)$ with
real-valued potential $V$, and let $H_0=-\Delta$. If $V$ has sufficient
pointwise decay, the wave operators $W_{\pm}=s-\lim_{t\to \pm\infty}
e^{itH}e^{-itH_0}$ are known to be bounded on $L^p(\mathbb R^4)$ for all $1\leq
p\leq \infty$ if zero is not an eigenvalue or resonance, and on $\frac43<p<4$
if zero is an eigenvalue but not a resonance. We show that in the latter case,
the wave operators are also bounded on $L^p(\mathbb R^4)$ for $1\leq p\leq
\frac43$ by direct examination of the integral kernel of the leading terms.
Furthermore, if $\int_{\mathbb R^4} xV(x) \psi(x) \, dx=0$ for all zero energy
eigenfunctions $\psi$, then the wave operators are bounded on $L^p$ for $1 \leq
p<\infty$.Comment: Updated references and made changes according to referee suggestions.
To appear in Annales Henri Poincare, 20 page | On the $L^p$ boundedness of wave operators for four-dimensional
Schr\"odinger Operators with a threshold eigenvalue | on the $l^p$ boundedness of wave operators for four-dimensional schr\"odinger operators with a threshold eigenvalue | delta schr odinger mathbb valued delta pointwise infty mathbb infty eigenvalue frac eigenvalue resonance. mathbb frac examination kernel terms. mathbb eigenfunctions infty .comment updated referee suggestions. annales henri poincare | non_dup | [] |
73390452 | 10.1007/s00023-016-0535-0 | The Ponzano-Regge state-sum model provides a quantization of 3d gravity as a
spin foam, providing a quantum amplitude to each 3d triangulation defined in
terms of the 6j-symbol (from the spin-recoupling theory of SU(2)
representations). In this context, the invariance of the 6j-symbol under 4-1
Pachner moves, mathematically defined by the Biedenharn-Elliot identity, can be
understood as the invariance of the Ponzano-Regge model under coarse-graining
or equivalently as the invariance of the amplitudes under the Hamiltonian
constraints. Here we look at length and volume insertions in the
Biedenharn-Elliot identity for the 6j-symbol, derived in some sense as higher
derivatives of the original formula. This gives the behavior of these
geometrical observables under coarse-graining. These new identities turn out to
be related to the Biedenharn-Elliot identity for the q-deformed 6j-symbol and
highlight that the q-deformation produces a cosmological constant term in the
Hamiltonian constraints of 3d quantum gravity.Comment: 18 page | 3d Quantum Gravity: Coarse-Graining and q-Deformation | 3d quantum gravity: coarse-graining and q-deformation | ponzano regge quantization foam triangulation symbol recoupling representations invariance symbol pachner moves mathematically biedenharn elliot understood invariance ponzano regge coarse graining equivalently invariance amplitudes constraints. look insertions biedenharn elliot symbol derivatives formula. geometrical observables coarse graining. identities biedenharn elliot deformed symbol highlight deformation produces cosmological | non_dup | [] |
42692142 | 10.1007/s00023-016-0536-z | The nonlinear Schrodinger (NLS) equation is considered on a periodic metric
graph subject to the Kirchhoff boundary conditions. Bifurcations of standing
localized waves for frequencies lying below the bottom of the linear spectrum
of the associated stationary Schrodinger equation are considered by using
analysis of two-dimensional discrete maps near hyperbolic fixed points. We
prove existence of two distinct families of small-amplitude standing localized
waves, which are symmetric about the two symmetry points of the periodic
graphs. We also prove properties of the two families, in particular, positivity
and exponential decay. The asymptotic reduction of the two-dimensional discrete
map to the stationary NLS equation on an infinite line is discussed in the
context of the homogenization of the NLS equation on the periodic metric graph.Comment: 23 page | Bifurcations of standing localized waves on periodic graphs | bifurcations of standing localized waves on periodic graphs | schrodinger kirchhoff conditions. bifurcations standing localized lying stationary schrodinger hyperbolic points. families standing localized graphs. families positivity exponential decay. asymptotic stationary infinite homogenization | non_dup | [] |
42714590 | 10.1007/s00023-016-0537-y | Single-shot quantum channel discrimination is a fundamental task in quantum
information theory. It is well known that entanglement with an ancillary system
can help in this task, and furthermore that an ancilla with the same dimension
as the input of the channels is always sufficient for optimal discrimination of
two channels. A natural question to ask is whether the same holds true for the
output dimension. That is, in cases when the output dimension of the channels
is (possibly much) smaller than the input dimension, is an ancilla with
dimension equal to the output dimension always sufficient for optimal
discrimination? We show that the answer to this question is "no" by
construction of a family of counterexamples. This family contains instances
with arbitrary finite gap between the input and output dimensions, and still
has the property that in every case, for optimal discrimination, it is
necessary to use an ancilla with dimension equal to that of the input.
The proof relies on a characterization of all operators on the trace norm
unit sphere that maximize entanglement negativity. In the case of density
operators we generalize this characterization to a broad class of entanglement
measures, which we call weak entanglement measures. This characterization
allows us to conclude that a quantum channel is reversible if and only if it
preserves entanglement as measured by any weak entanglement measure, with the
structure of maximally entangled states being equivalent to the structure of
reversible maps via the Choi isomorphism. We also include alternate proofs of
other known characterizations of channel reversibility.Comment: v2: updated references and minor modifications; in Annales Henri
Poincare, November 201 | Ancilla dimension in quantum channel discrimination | ancilla dimension in quantum channel discrimination | shot discrimination theory. entanglement ancillary ancilla discrimination channels. dimension. possibly ancilla discrimination answer counterexamples. instances discrimination ancilla input. relies trace norm sphere maximize entanglement negativity. generalize broad entanglement call entanglement measures. reversible preserves entanglement entanglement maximally entangled reversible choi isomorphism. alternate proofs characterizations updated minor modifications annales henri poincare november | non_dup | [] |
42686428 | 10.1007/s00023-016-0539-9 | We study the evolution of a driven harmonic oscillator with a time-dependent
frequency $\omega_t \propto |t|$. At time $t=0$ the Hamiltonian undergoes a
point of infinite spectral degeneracy. If the system is initialized in the
instantaneous vacuum in the distant past then the asymptotic future state is a
squeezed state whose parameters are explicitly determined. We show that the
squeezing is independent on the sweeping rate. This manifests the failure of
the adiabatic approximation at points where infinitely many eigenvalues
collide. We extend our analysis to the situation where the gap at $t=0$ remains
finite. We also discuss the natural geometry of the manifold of squeezed
states. We show that it is realized by the Poincar\'e disk model viewed as a
K\"ahler manifold | Dynamical crossing of an infinitely degenerate critical point | dynamical crossing of an infinitely degenerate critical point | harmonic oscillator omega propto undergoes infinite degeneracy. initialized instantaneous distant asymptotic squeezed explicitly determined. squeezing sweeping rate. manifests adiabatic infinitely eigenvalues collide. extend finite. manifold squeezed states. realized poincar viewed ahler manifold | non_dup | [] |
42703759 | 10.1007/s00023-016-0541-2 | We study the application of Kasparov theory to topological insulator systems
and the bulk-edge correspondence. We consider observable algebras as modelled
by crossed products, where bulk and edge systems may be linked by a short exact
sequence. We construct unbounded Kasparov modules encoding the dynamics of the
crossed product. We then link bulk and edge Kasparov modules using the Kasparov
product. Because of the anti-linear symmetries that occur in topological
insulator models, real $C^*$-algebras and $KKO$-theory must be used.Comment: Minor corrections, to appear in Annales Henri Poincar\' | The $K$-theoretic bulk-edge correspondence for topological insulators | the $k$-theoretic bulk-edge correspondence for topological insulators | kasparov topological insulator correspondence. observable algebras modelled crossed sequence. unbounded kasparov modules encoding crossed product. kasparov modules kasparov product. symmetries topological insulator algebras minor annales henri poincar | non_dup | [] |
42748879 | 10.1007/s00023-016-0548-8 | We study a reversible continuous-time Markov dynamics on lozenge tilings of
the plane, introduced by Luby et al. Single updates consist in concatenations
of $n$ elementary lozenge rotations at adjacent vertices. The dynamics can also
be seen as a reversible stochastic interface evolution. When the update rate is
chosen proportional to $1/n$, the dynamics is known to enjoy especially nice
features: a certain Hamming distance between configurations contracts with time
on average and the relaxation time of the Markov chain is diffusive, growing
like the square of the diameter of the system. Here, we present another
remarkable feature of this dynamics, namely we derive, in the diffusive time
scale, a fully explicit hydrodynamic limit equation for the height function (in
the form of a non-linear parabolic PDE). While this equation cannot be written
as a gradient flow w.r.t. a surface energy functional, it has nice analytic
properties, for instance it contracts the $\mathbb L^2$ distance between
solutions. The mobility coefficient $\mu$ in the equation has non-trivial but
explicit dependence on the interface slope and, interestingly, is directly
related to the system's surface free energy. The derivation of the hydrodynamic
limit is not fully rigorous, in that it relies on an unproven assumption of
local equilibrium.Comment: 31 pages, 8 figures. v2: typos corrected, some proofs clarified. To
appear on Annales Henri Poincar | Hydrodynamic limit equation for a lozenge tiling Glauber dynamics | hydrodynamic limit equation for a lozenge tiling glauber dynamics | reversible markov lozenge tilings luby updates consist concatenations elementary lozenge rotations adjacent vertices. reversible stochastic evolution. update enjoy nice hamming configurations contracts relaxation markov diffusive growing system. remarkable derive diffusive hydrodynamic parabolic w.r.t. nice analytic contracts mathbb solutions. mobility trivial interestingly energy. derivation hydrodynamic rigorous relies unproven pages figures. typos corrected proofs clarified. annales henri poincar | non_dup | [] |
73350508 | 10.1007/s00023-016-0549-7 | We apply Feshbach-Krein-Schur renormalization techniques in the hierarchical
Anderson model to establish a criterion on the single-site distribution which
ensures exponential dynamical localization as well as positive inverse
participation ratios and Poisson statistics of eigenvalues. Our criterion
applies to all cases of exponentially decaying hierarchical hopping strengths
and holds even for spectral dimension $d > 2$, which corresponds to the regime
of transience of the underlying hierarchical random walk. This challenges
recent numerical findings that the spectral dimension is significant as far as
the Anderson transition is concerned | Renormalization Group Analysis of the Hierarchical Anderson Model | renormalization group analysis of the hierarchical anderson model | feshbach krein schur renormalization hierarchical anderson establish criterion ensures exponential localization participation poisson eigenvalues. criterion applies exponentially decaying hierarchical hopping strengths transience hierarchical walk. challenges anderson concerned | non_dup | [] |
42665964 | 10.1007/s00023-017-0550-9 | We prove that the quantum relative entropy decreases monotonically under the
application of any positive trace-preserving linear map, for underlying
separable Hilbert spaces. This answers in the affirmative a natural question
that has been open for a long time, as monotonicity had previously only been
shown to hold under additional assumptions, such as complete positivity or
Schwarz-positivity of the adjoint map. The first step in our proof is to show
monotonicity of the sandwiched Renyi divergences under positive
trace-preserving maps, extending a proof of the data processing inequality by
Beigi [J. Math. Phys. 54, 122202 (2013)] that is based on complex interpolation
techniques. Our result calls into question several measures of non-Markovianity
that have been proposed, as these would assess all positive trace-preserving
time evolutions as Markovian.Comment: v3: published version; v2: 9 pages, extended results to infinite
dimensions and lifted trace-preservation condition, added discussions and
references; v1: 5 page | Monotonicity of the Quantum Relative Entropy Under Positive Maps | monotonicity of the quantum relative entropy under positive maps | monotonically trace preserving separable hilbert spaces. answers affirmative monotonicity hold assumptions positivity schwarz positivity adjoint map. monotonicity sandwiched renyi divergences trace preserving extending inequality beigi math. phys. interpolation techniques. calls markovianity trace preserving evolutions pages infinite lifted trace preservation discussions | non_dup | [] |
73351585 | 10.1007/s00023-017-0558-1 | We call \emph{Alphabet model} a generalization to N types of particles of the
classic ABC model. We have particles of different types stochastically evolving
on a one dimensional lattice with an exchange dynamics. The rates of exchange
are local but under suitable conditions the dynamics is reversible with a
Gibbsian like invariant measure with long range interactions. We discuss
geometrically the conditions of reversibility on a ring that correspond to a
gradient condition on the graph of configurations or equivalently to a
divergence free condition on a graph structure associated to the types of
particles. We show that much of the information on the interactions between
particles can be encoded in associated \emph{Tournaments} that are a special
class of oriented directed graphs. In particular we show that the interactions
of reversible models are corresponding to strongly connected tournaments. The
possible minimizers of the energies are in correspondence with the Hamiltonian
cycles of the tournaments. We can then determine how many and which are the
possible minimizers of the energy looking at the structure of the associated
tournament. As a byproduct we obtain a probabilistic proof of a classic Theorem
of Camion \cite{Camion} on the existence of Hamiltonian cycles for strongly
connected tournaments. Using these results we obtain in the case of an equal
number of k types of particles new representations of the Hamiltonians in terms
of translation invariant $k$-body long range interactions. We show that when
$k=3,4$ the minimizer of the energy is always unique up to translations.
Starting from the case $k=5$ it is possible to have more than one minimizer. In
particular it is possible to have minimizers for which particles of the same
type are not joined together in single clusters.Comment: Reorganized according to referees report, new example | The energy of the alphabet model | the energy of the alphabet model | call emph alphabet generalization classic model. stochastically evolving dynamics. reversible gibbsian interactions. geometrically reversibility configurations equivalently divergence particles. encoded emph tournaments oriented directed graphs. reversible tournaments. minimizers correspondence cycles tournaments. minimizers looking tournament. byproduct probabilistic classic camion cite camion cycles tournaments. representations hamiltonians translation interactions. minimizer translations. minimizer. minimizers joined reorganized referees | non_dup | [] |
42746213 | 10.1007/s00023-017-0562-5 | We consider a spherical spin system with pure 2-spin spherical
Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction.
The system shows a two-dimensional phase transition with respect to the
temperature and the coupling constant. We compute the limiting distributions of
the free energy for all parameters away from the critical values. The zero
temperature case corresponds to the well-known phase transition of the largest
eigenvalue of a rank 1 spiked random symmetric matrix. As an intermediate step,
we establish a central limit theorem for the linear statistics of rank 1 spiked
random symmetric matrices.Comment: 45 pages, references adde | Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick
model with ferromagnetic interaction | fluctuations of the free energy of the spherical sherrington-kirkpatrick model with ferromagnetic interaction | spherical spherical sherrington kirkpatrick ferromagnetic curie weiss interaction. constant. limiting away values. eigenvalue spiked matrix. establish spiked pages adde | non_dup | [] |
73369371 | 10.1007/s00023-017-0569-y | We show that recent multivariate generalizations of the Araki-Lieb-Thirring
inequality and the Golden-Thompson inequality [Sutter, Berta, and Tomamichel,
Comm. Math. Phys. (2016)] for Schatten norms hold more generally for all
unitarily invariant norms and certain variations thereof. The main technical
contribution is a generalization of the concept of log-majorization which
allows us to treat majorization with regards to logarithmic integral averages
of vectors of singular values.Comment: 17 page | Generalized Log-Majorization and Multivariate Trace Inequalities | generalized log-majorization and multivariate trace inequalities | multivariate generalizations araki lieb thirring inequality golden thompson inequality sutter berta tomamichel comm. math. phys. schatten norms hold unitarily norms thereof. generalization majorization treat majorization regards logarithmic averages singular | non_dup | [] |
42744866 | 10.1007/s00023-017-0572-3 | We consider a two dimensional random band matrix ensemble, in the limit of
infinite volume and fixed but large band width $W$. For this model we
rigorously prove smoothness of the averaged density of states. We also prove
that the resulting expression coincides with Wigner's semicircle law with a
precision $W^{-2+\delta },$ where $\delta\to 0$ when $W\to \infty.$ The proof
uses the supersymmetric approach and extends results by Disertori, Pinson and
Spencer from three to two dimensions.Comment: 41 pages, 2 figure | Density of States for Random Band Matrices in two dimensions | density of states for random band matrices in two dimensions | ensemble infinite rigorously smoothness averaged states. coincides wigner semicircle precision delta delta infty. supersymmetric extends disertori pinson spencer pages | non_dup | [] |
73376786 | 10.1007/s00023-017-0577-y | We introduce and study a category $\text{Fin}$ of modules of the Borel
subalgebra of a quantum affine algebra $U_q\mathfrak{g}$, where the commutative
algebra of Drinfeld generators $h_{i,r}$, corresponding to Cartan currents, has
finitely many characteristic values. This category is a natural extension of
the category of finite-dimensional $U_q\mathfrak{g}$ modules. In particular, we
classify the irreducible objects, discuss their properties, and describe the
combinatorics of the q-characters. We study transfer matrices corresponding to
modules in $\text{Fin}$. Among them we find the Baxter $Q_i$ operators and
$T_i$ operators satisfying relations of the form $T_iQ_i=\prod_j Q_j+ \prod_k
Q_k$. We show that these operators are polynomials of the spectral parameter
after a suitable normalization. This allows us to prove the Bethe ansatz
equations for the zeroes of the eigenvalues of the $Q_i$ operators acting in an
arbitrary finite-dimensional representation of $U_q\mathfrak{g}$.Comment: Latex 33 page | Finite type modules and Bethe ansatz equations | finite type modules and bethe ansatz equations | modules borel subalgebra affine mathfrak commutative drinfeld generators cartan currents finitely values. mathfrak modules. classify irreducible combinatorics characters. modules baxter satisfying prod prod polynomials normalization. bethe ansatz zeroes eigenvalues acting mathfrak .comment latex | non_dup | [] |
42705528 | 10.1007/s00023-017-0578-x | We extend to the two-particle Anderson model the characterization of the
metal-insulator transport transition obtained in the one-particle setting by
Germinet and Klein. We show that, for any fixed number of particles, the slow
spreading of wave packets in time implies the initial estimate of a modified
version of the Bootstrap Multiscale Analysis. In this new version, operators
are restricted to boxes defined with respect to the pseudo-distance in which we
have the slow spreading. At the bottom of the spectrum, within the regime of
one-particle dynamical localization, we show that this modified multiscale
analysis yields dynamical localization for the two-particle Anderson model,
allowing us to obtain a characterization of the metal-insulator transport
transition for the two-particle Anderson model at the bottom of the spectrum | Characterization of the metal-insulator transport transition for the
two-particle Anderson model | characterization of the metal-insulator transport transition for the two-particle anderson model | extend anderson insulator germinet klein. slow spreading packets bootstrap multiscale analysis. restricted boxes pseudo slow spreading. localization multiscale localization anderson allowing insulator anderson | non_dup | [] |
80851261 | 10.1007/s00023-017-0579-9 | Following an earlier similar conjecture of Kellendonk and Putnam, Giordano, Putnam, and Skau conjectured that all minimal, free ZdZd actions on Cantor sets admit “small cocycles.” These represent classes in H1H1 that are mapped to small vectors in RdRd by the Ruelle–Sullivan (RS) map. We show that there exist Z2Z2 actions where no such small cocycles exist, and where the image of H1H1 under RS is Z2Z2 . Our methods involve tiling spaces and shape deformations, and along the way we prove a relation between the image of RS and the set of “virtual eigenvalues,” i.e., elements of RdRd that become topological eigenvalues of the tiling flow after an arbitrarily small change in the shapes and sizes of the tiles.Peer-reviewedPublisher Versio | Small Cocycles, Fine Torus Fibrations, and a Z^2 Subshift with Neither | small cocycles, fine torus fibrations, and a z^2 subshift with neither | conjecture kellendonk putnam giordano putnam skau conjectured zdzd cantor admit “small cocycles.” mapped rdrd ruelle–sullivan map. cocycles involve tiling deformations “virtual eigenvalues i.e. rdrd topological eigenvalues tiling arbitrarily shapes sizes tiles.peer reviewedpublisher versio | non_dup | [] |
73353794 | 10.1007/s00023-017-0580-3 | We study the propagation of bosonic strings in singular target space-times.
For describing this, we assume this target space to be the quotient of a smooth
manifold $M$ by a singular foliation ${\cal F}$ on it. Using the technical tool
of a gauge theory, we propose a smooth functional for this scenario, such that
the propagation is assured to lie in the singular target on-shell, i.e. only
after taking into account the gauge invariant content of the theory. One of the
main new aspects of our approach is that we do not limit ${\cal F}$ to be
generated by a group action. We will show that, whenever it exists, the above
gauging is effectuated by a single geometrical and universal gauge theory,
whose target space is the generalized tangent bundle $TM\oplus T^*M$.Comment: 49 pages, 4 figure | Strings in Singular Space-Times and their Universal Gauge Theory | strings in singular space-times and their universal gauge theory | propagation bosonic strings singular times. describing quotient manifold singular foliation propose propagation assured singular i.e. theory. action. whenever gauging effectuated geometrical universal tangent bundle oplus .comment pages | non_dup | [] |
73394698 | 10.1007/s00023-017-0582-1 | We establish inequalities relating the size of a material body to its mass,
angular momentum, and charge, within the context of axisymmetric initial data
sets for the Einstein equations. These inequalities hold in general without the
assumption of the maximal condition, and use a notion of size which is easily
computable. Moreover, these results give rise to black hole existence criteria
which are meaningful even in the time-symmetric case, and also include certain
boundary effects.Comment: 12 page | Inequalities Between Size, Mass, Angular Momentum, and Charge for
Axisymmetric Bodies and the Formation of Trapped Surfaces | inequalities between size, mass, angular momentum, and charge for axisymmetric bodies and the formation of trapped surfaces | establish inequalities relating axisymmetric einstein equations. inequalities hold maximal notion computable. meaningful | non_dup | [] |
42749837 | 10.1007/s00023-017-0586-x | In an abstract framework, a new concept on time operator, ultra-weak time
operator, is introduced, which is a concept weaker than that of weak time
operator. Theorems on the existence of an ultra-weak time operator are
established. As an application of the theorems, it is shown that Schroedinger
operators H with potentials V obeying suitable conditions, including the
Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a
class of Borel measurable functions $f$ such that $f(H)$ has an ultra-weak time
operator is found.Comment: We add Sections 1.1,1.2 and 1. | Ultra-Weak Time Operators of Schroedinger Operators | ultra-weak time operators of schroedinger operators | ultra weaker operator. theorems ultra established. theorems schroedinger potentials obeying atom ultra operators. borel measurable ultra | non_dup | [] |
73385685 | 10.1007/s00023-017-0588-8 | In this paper we research all possible finite-dimensional representations and
corresponding values of the Barbero-Immirzi parameter contained in EPRL
simplicity constraints by using Naimark's fundamental theorem of the Lorentz
group representation theory. It turns out that for each non-zero pure imaginary
with rational modulus value of the Barbero-Immirzi parameter $\gamma = i
\frac{p}{q}, p, q \in Z, p, q \ne 0$, there is a solution of the simplicity
constraints, such that the corresponding Lorentz representation is finite
dimensional. The converse is also true - for each finite-dimensional Lorentz
representation solution of the simplicity constraints $(n, \rho)$, the
associated Barbero-Immirzi parameter is non-zero pure imaginary with rational
modulus, $\gamma = i \frac{p}{q}, p, q \in Z, p, q \ne 0$. We solve the
simplicity constraints with respect to the Barbero-Immirzi parameter and then
use Naimark's fundamental theorem of the Lorentz group representations to find
all finite-dimensional representations contained in the solutions | Revisiting EPRL: All Finite-Dimensional Solutions by Naimark's
Fundamental Theorem | revisiting eprl: all finite-dimensional solutions by naimark's fundamental theorem | representations barbero immirzi eprl simplicity naimark lorentz theory. turns imaginary rational modulus barbero immirzi gamma frac simplicity lorentz dimensional. converse lorentz simplicity barbero immirzi imaginary rational modulus gamma frac solve simplicity barbero immirzi naimark lorentz representations representations | non_dup | [] |
83835342 | 10.1007/s00023-017-0591-0 | We study a one-dimensional quantum system with an arbitrary number of
hard-core particles on the lattice, which are subject to a deterministic
attractive interaction as well as a random potential. Our choice of interaction
is suggested by the spectral analysis of the XXZ quantum spin chain. The main
result concerns a version of high-disorder Fock-space localization expressed
here in the configuration space of hard-core particles. The proof relies on an
energetically motivated Combes-Thomas estimate and an effective one-particle
analysis. As an application, we show the exponential decay of the two-point
function in the infinite system uniformly in the particle number.Comment: 24 page | Low-energy Fock-space localization for attractive hard-core particles in
disorder | low-energy fock-space localization for attractive hard-core particles in disorder | deterministic attractive potential. chain. concerns disorder fock localization particles. relies energetically motivated combes thomas analysis. exponential infinite uniformly | non_dup | [] |
42746142 | 10.1007/s00023-017-0592-z | Motivated by the Strong Cosmic Censorship Conjecture, in the presence of a
cosmological constant, we consider solutions of the scalar wave equation
$\Box_g\phi=0$ on fixed subextremal Reissner--Nordstr\"om--de Sitter
backgrounds $({\mathcal M}, g)$, without imposing symmetry assumptions on
$\phi$. We provide a sufficient condition, in terms of surface gravities and a
parameter for an exponential decaying Price law, for a local energy of the
waves to remain bounded up to the Cauchy horizon. The energy we consider
controls, in particular, regular transverse derivatives at the Cauchy horizon;
this allows us to extend the solutions with bounded energy, to the Cauchy
horizon, as functions in $C^0\cap H^1_{loc}$. Our results correspond to another
manifestation of the potential breakdown of Strong Cosmic Censorship in the
positive cosmological constant setting.Comment: 21 pages, 5 figure | Bounded energy waves on the black hole interior of
Reissner-Nordstr\"om-de Sitter | bounded energy waves on the black hole interior of reissner-nordstr\"om-de sitter | motivated cosmic censorship conjecture cosmological subextremal reissner nordstr sitter backgrounds mathcal imposing assumptions gravities exponential decaying cauchy horizon. derivatives cauchy horizon extend cauchy horizon manifestation breakdown cosmic censorship cosmological pages | non_dup | [] |
73440061 | 10.1007/s00023-017-0593-y | Abelian duality is realized naturally by combining differential cohomology
and locally covariant quantum field theory. This leads to a C$^*$-algebra of
observables, which encompasses the simultaneous discretization of both magnetic
and electric fluxes. We discuss the assignment of physically well-behaved
states to such algebra and the properties of the associated GNS triple. We show
that the algebra of observables factorizes as a suitable tensor product of
three C$^*$-algebras: the first factor encodes dynamical information, while the
other two capture topological data corresponding to electric and magnetic
fluxes. On the former factor we exhibit a state whose two-point correlation
function has the same singular structure of a Hadamard state. Specifying
suitable counterparts also on the topological factors we obtain a state for the
full theory, providing ultimately a unitary implementation of Abelian duality.Comment: 33 page | Hadamard states for quantum Abelian duality | hadamard states for quantum abelian duality | abelian duality realized naturally combining cohomology locally covariant theory. observables encompasses simultaneous discretization fluxes. assignment physically behaved triple. observables factorizes algebras encodes capture topological fluxes. former exhibit singular hadamard state. specifying counterparts topological ultimately unitary abelian | non_dup | [] |
73360039 | 10.1007/s00023-017-0594-x | We begin with a basic exploration of the (point-set topological) notion of
Hausdorff closed limits in the spacetime setting. Specifically, we show that
this notion of limit is well suited to sequences of achronal sets, and use this
to generalize the `achronal limits' introduced in [12]. This, in turn, allows
for a broad generalization of the notion of Lorentzian horosphere introduced in
[12]. We prove a new rigidity result for such horospheres, which in a sense
encodes various spacetime splitting results, including the basic Lorentzian
splitting theorem. We use this to give a partial proof of the Bartnik splitting
conjecture, under a new condition involving past and future Cauchy horospheres,
which is weaker than those considered in [10] and [12]. We close with some
observations on spacetimes with spacelike causal boundary, including a rigidity
result in the positive cosmological constant case.Comment: 29 pages, 5 figure | Hausdorff closed limits and rigidity in Lorentzian geometry | hausdorff closed limits and rigidity in lorentzian geometry | begin exploration topological notion hausdorff spacetime setting. notion suited achronal generalize achronal broad generalization notion lorentzian horosphere rigidity horospheres encodes spacetime splitting lorentzian splitting theorem. bartnik splitting conjecture involving cauchy horospheres weaker spacetimes spacelike causal rigidity cosmological pages | non_dup | [] |
73385937 | 10.1007/s00023-017-0595-9 | Starting from a $d\times d$ rational Lax pair system of the form $\hbar
\partial_x \Psi= L\Psi$ and $\hbar \partial_t \Psi=R\Psi$ we prove that, under
certain assumptions (genus $0$ spectral curve and additional conditions on $R$
and $L$), the system satisfies the "topological type property". A consequence
is that the formal $\hbar$-WKB expansion of its determinantal correlators,
satisfy the topological recursion. This applies in particular to all $(p,q)$
minimal models reductions of the KP hierarchy, or to the six Painlev\'e
systems.Comment: Published version in Annales Henri Poincar\' | Integrable differential systems of topological type and reconstruction
by the topological recursion | integrable differential systems of topological type and reconstruction by the topological recursion | rational hbar hbar assumptions genus satisfies topological formal hbar determinantal correlators satisfy topological recursion. applies reductions hierarchy painlev annales henri poincar | non_dup | [] |
73387510 | 10.1007/s00023-017-0597-7 | Open Quantum Walks (OQWs), originally introduced by S. Attal, are quantum
generalizations of classical Markov chains. Recently, natural continuous time
models of OQW have been developed by C. Pellegrini. These models, called
Continuous Time Open Quantum Walks (CTOQWs), appear as natural continuous time
limits of discrete time OQWs. In particular they are quantum extensions of
continuous time Markov chains. This article is devoted to the study of
homogeneous CTOQW on $\mathbb{Z}^d$. We focus namely on their associated
quantum trajectories which allow us to prove a Central Limit Theorem for the
"position" of the walker as well as a Large Deviation Principle.Comment: 31 pages, 5 figure | Central Limit Theorem and Large Deviation Principle for Continuous Time
Open Quantum Walks | central limit theorem and large deviation principle for continuous time open quantum walks | walks oqws originally attal generalizations markov chains. pellegrini. walks ctoqws oqws. extensions markov chains. devoted homogeneous ctoqw mathbb trajectories walker pages | non_dup | [] |
83865671 | 10.1007/s00023-017-0598-6 | In this article, we study the quantum theory of gravitational boundary modes
on a null surface. These boundary modes are given by a spinor and a
spinor-valued two-form, which enter the gravitational boundary term for
self-dual gravity. Using a Fock representation, we quantise the boundary
fields, and show that the area of a two-dimensional cross section turns into
the difference of two number operators. The spectrum is discrete, and it agrees
with the one known from loop quantum gravity with the correct dependence on the
Barbero--Immirzi parameter. No discrete structures (such as spin network
functions, or triangulations of space) are ever required---the entire
derivation happens at the level of the continuum theory. In addition, the area
spectrum is manifestly Lorentz invariant.Comment: 27 pages, two figure | Fock representation of gravitational boundary modes and the discreteness
of the area spectrum | fock representation of gravitational boundary modes and the discreteness of the area spectrum | gravitational surface. spinor spinor valued enter gravitational gravity. fock quantise turns operators. agrees barbero immirzi parameter. triangulations ever derivation happens continuum theory. manifestly lorentz pages | non_dup | [] |
42659746 | 10.1007/s00023-017-0599-5 | We consider the Cauchy problem of 2+1 equivariant wave maps coupled to
Einstein's equations of general relativity and prove that two separate
(nonlinear) subclasses of the system disperse to their corresponding linearized
equations in the large. Global asymptotic behaviour of 2+1 Einstein-wave map
system is relevant because the system occurs naturally in 3+1 vacuum Einstein's
equations.Comment: Error from a previous work (Lemma 9.1 in Ref[1]) rectified. Original
problem reduced to two special case | On Scattering for Small Data of 2+1 Dimensional Equivariant
Einstein-Wave Map System | on scattering for small data of 2+1 dimensional equivariant einstein-wave map system | cauchy equivariant einstein relativity subclasses disperse linearized large. asymptotic einstein naturally einstein rectified. | non_dup | [] |
83860575 | 10.1007/s00023-017-0600-3 | A hyperlink is a finite set of non-intersecting simple closed curves in
$\mathbb{R} \times \mathbb{R}^3$. Let $S$ be an orientable surface in
$\mathbb{R}^3$. The dynamical variables in General Relativity are the vierbein
$e$ and a $\mathfrak{su}(2)\times\mathfrak{su}(2)$-valued connection $\omega$.
Together with Minkowski metric, $e$ will define a metric $g$ on the manifold.
Denote $A_S(e)$ as the area of $S$, for a given choice of $e$.
The Einstein-Hilbert action $S(e,\omega)$ is defined on $e$ and $\omega$. We
will quantize the area of the surface $S$ by integrating $A_S(e)$ against a
holonomy operator of a hyperlink $L$, disjoint from $S$, and the exponential of
the Einstein-Hilbert action, over the space of vierbeins $e$ and
$\mathfrak{su}(2)\times\mathfrak{su}(2)$-valued connections $\omega$. Using our
earlier work done on Chern-Simons path integrals in $\mathbb{R}^3$, we will
write this infinite dimensional path integral as the limit of a sequence of
Chern-Simons integrals. Our main result shows that the area operator can be
computed from a link-surface diagram between $L$ and $S$. By assigning an
irreducible representation of $\mathfrak{su}(2)\times\mathfrak{su}(2)$ to each
component of $L$, the area operator gives the total net momentum impact on the
surface $S$.Comment: arXiv admin note: text overlap with arXiv:1701.04397,
arXiv:1705.0039 | Area Operator in Loop Quantum Gravity | area operator in loop quantum gravity | hyperlink intersecting mathbb mathbb orientable mathbb relativity vierbein mathfrak mathfrak valued connection omega minkowski manifold. einstein hilbert omega omega quantize integrating holonomy hyperlink disjoint exponential einstein hilbert vierbeins mathfrak mathfrak valued connections omega chern simons integrals mathbb infinite chern simons integrals. assigning irreducible mathfrak mathfrak .comment admin overlap | non_dup | [] |
73348365 | 10.1007/s00023-017-0601-2 | A finite discrete graph is turned into a quantum (metric) graph once a finite
length is assigned to each edge and the one-dimensional Laplacian is taken to
be the operator. We study the dependence of the spectral gap (the first
positive Laplacian eigenvalue) on the choice of edge lengths. In particular,
starting from a certain discrete graph, we seek the quantum graph for which an
optimal (either maximal or minimal) spectral gap is obtained. We fully solve
the minimization problem for all graphs. We develop tools for investigating the
maximization problem and solve it for some families of graphs | Quantum graphs which optimize the spectral gap | quantum graphs which optimize the spectral gap | turned assigned laplacian operator. laplacian eigenvalue lengths. seek maximal obtained. solve minimization graphs. investigating maximization solve families | non_dup | [] |
73390908 | 10.1007/s00023-017-0602-1 | The existence, established over the past number of years and supporting
earlier work of Ori [14], of physically relevant black hole spacetimes that
admit $C^0$ metric extensions beyond the future Cauchy horizon, while being
$C^2$-inextendible, has focused attention on fundamental issues concerning the
strong cosmic censorship conjecture. These issues were recently discussed in
the work of Jan Sbierski [17], in which he established the (nonobvious) fact
that the Schwarschild solution in global Kruskal-Szekeres coordinates is
$C^0$-inextendible. In this paper we review aspects of Sbierski's methodology
in a general context, and use similar techniques, along with some new
observations, to consider the $C^0$-inextendibility of open FLRW cosmological
models. We find that a certain special class of open FLRW spacetimes, which we
have dubbed `Milne-like,' actually admit $C^0$ extensions through the big bang.
For spacetimes that are not Milne-like, we prove some inextendibility results
within the class of spherically symmetric spacetimes.Comment: 22 pages, v2: minor changes and clarifications; reference added. To
appear in Annales Henri Poincar | Some Remarks on the $C^0$-(in)extendibility of Spacetimes | some remarks on the $c^0$-(in)extendibility of spacetimes | supporting physically spacetimes admit extensions cauchy horizon inextendible focused concerning cosmic censorship conjecture. sbierski nonobvious schwarschild kruskal szekeres inextendible. sbierski methodology inextendibility flrw cosmological models. flrw spacetimes dubbed milne admit extensions bang. spacetimes milne inextendibility spherically pages minor clarifications added. annales henri poincar | non_dup | [] |
42717643 | 10.1007/s00023-017-0603-0 | For a massless free scalar field in a globally hyperbolic space-time we
compare the global temperature T, defined for the KMS states $\omega^T$, with
the local temperature $T_{\omega}(x)$ introduced by Buchholz and Schlemmer. We
prove the following claims: (1) Whenever $T_{\omega^T}(x)$ is defined, it is a
continuous, monotonically increasing function of T at every point x. (2)
$T_{\omega}(x)$ is defined when the space-time is ultra-static with compact
Cauchy surface and non-trivial scalar curvature $R\ge 0$, $\omega$ is
stationary and a few other assumptions are satisfied. Our proof of (2) relies
on the positive mass theorem. We discuss the necessity of its assumptions,
providing counter-examples in an ultra-static space-time with non-compact
Cauchy surface and R<0 somewhere. We interpret the result in terms of a
violation of the weak energy condition in the background space-time.Comment: 19 pages; v2 accepted for publicatio | Local vs. global temperature under a positive curvature condition | local vs. global temperature under a positive curvature condition | massless globally hyperbolic omega omega buchholz schlemmer. claims whenever omega monotonically omega ultra cauchy trivial curvature omega stationary assumptions satisfied. relies theorem. necessity assumptions counter ultra cauchy somewhere. interpret violation pages publicatio | non_dup | [] |
73376905 | 10.1007/s00023-017-0604-z | We consider the problem of deciding if a set of quantum one-qudit gates
$\mathcal{S}=\{g_1,\ldots,g_n\}\subset G$ is universal, i.e if the closure
$\overline{<\mathcal{S}>}$ is equal to $G$, where $G$ is either the special
unitary or the special orthogonal group. To every gate $g$ in $\mathcal{S}$ we
asign its image under the adjoint representation $\mathrm{Ad}_g$, where
$\mathrm{Ad}:G\rightarrow SO(\mathfrak{g})$ and $\mathfrak{g}$ is the Lie
algebra of $G$. The necessary condition for the universality of $\mathcal{S}$
is that the only matrices that commute with all $\mathrm{Ad}_{g_i}$'s are
proportional to the identity. If in addition there is an element in
$<\mathcal{S}>$ whose Hilbert-Schmidt distance from the centre of $G$ belongs
to $]0,\frac{1}{\sqrt{2}}]$, then $\mathcal{S}$ is universal. Using these we
provide a simple algorithm that allows deciding the universality of any set of
$d$-dimensional gates in a finite number of steps and formulate the general
classification theorem.Comment: Significantly improved universality criteria and presentation. A
simple algorithm that allows deciding the universality of any set of gates in
a finite number of steps added and discussed. Accepted in AH | Universality of single qudit gates | universality of single qudit gates | deciding qudit gates mathcal ldots universal closure overline mathcal unitary orthogonal group. gate mathcal asign adjoint mathrm mathrm rightarrow mathfrak mathfrak universality mathcal commute mathrm identity. mathcal hilbert schmidt belongs frac sqrt mathcal universal. deciding universality gates formulate universality presentation. deciding universality gates discussed. | non_dup | [] |
73375617 | 10.1007/s00023-017-0606-x | We describe the construction of a geometric invariant characterising initial
data for the Kerr-Newman spacetime. This geometric invariant vanishes if and
only if the initial data set corresponds to exact Kerr-Newman initial data, and
so characterises this type of data. We first illustrate the characterisation of
the Kerr-Newman spacetime in terms of Killing spinors. The space spinor
formalism is then used to obtain a set of four independent conditions on an
initial Cauchy hypersurface that guarantee the existence of a Killing spinor on
the development of the initial data. Following a similar analysis in the vacuum
case, we study the properties of solutions to the approximate Killing spinor
equation and use them to construct the geometric invariant.Comment: 34 page | A geometric invariant characterising initial data for the Kerr-Newman
spacetime | a geometric invariant characterising initial data for the kerr-newman spacetime | geometric characterising kerr newman spacetime. geometric vanishes kerr newman characterises data. illustrate characterisation kerr newman spacetime killing spinors. spinor formalism cauchy hypersurface guarantee killing spinor data. approximate killing spinor geometric | non_dup | [] |
42711555 | 10.1007/s00023-017-0607-9 | This paper continues the investigation of the formation of naked
singularities in the collapse of collisionless matter initiated in [RV]. There
the existence of certain classes of non-smooth solutions of the Einstein-Vlasov
system was proved. Those solutions are self-similar and hence not
asymptotically flat. To obtain solutions which are more physically relevant it
makes sense to attempt to cut off these solutions in a suitable way so as to
make them asymptotically flat. This task, which turns out to be technically
challenging, will be carried out in this paper.
[RV] A. D. Rendall and J. J. L. Vel\'{a}zquez, A class of dust-like
self-similar solutions of the massless Einstein-Vlasov system. Annales Henri
Poincare 12, 919-964, (2011).Comment: 67 pages, 1 figur | Veiled singularities for the spherically symmetric massless
Einstein-Vlasov system | veiled singularities for the spherically symmetric massless einstein-vlasov system | continues naked singularities collapse collisionless initiated einstein vlasov proved. asymptotically flat. physically attempt asymptotically flat. turns technically challenging paper. rendall zquez massless einstein vlasov system. annales henri poincare .comment pages figur | non_dup | [] |
83832799 | 10.1007/s00023-017-0608-8 | We consider a three-particle quantum system in dimension three composed of
two identical fermions of mass one and a different particle of mass $m$. The
particles interact via two-body short range potentials. We assume that the
Hamiltonians of all the two-particle subsystems do not have bound states with
negative energy and, moreover, that the Hamiltonians of the two subsystems made
of a fermion and the different particle have a zero-energy resonance. Under
these conditions and for $m<m^* = (13.607)^{-1}$, we give a rigorous proof of
the occurrence of the Efimov effect, i.e., the existence of infinitely many
negative eigenvalues for the three-particle Hamiltonian $H$. More precisely, we
prove that for $m>m^*$ the number of negative eigenvalues of $H$ is finite and
for $m<m^*$ the number $N(z)$ of negative eigenvalues of $H$ below $z<0$ has
the asymptotic behavior $N(z) \sim \mathcal C(m) |\log|z||$ for $z \rightarrow
0^-$. Moreover, we give an upper and a lower bound for the positive constant
$\mathcal C(m)$.Comment: 26 page | Efimov effect for a three-particle system with two identical fermions | efimov effect for a three-particle system with two identical fermions | composed fermions interact potentials. hamiltonians subsystems hamiltonians subsystems fermion resonance. rigorous occurrence efimov i.e. infinitely eigenvalues precisely eigenvalues eigenvalues asymptotic mathcal rightarrow mathcal .comment | non_dup | [] |
42719149 | 10.1007/s00023-017-0609-7 | We prove that estimating the ground state energy of a
translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is
QMAEXP-complete, even for systems of low local dimension (roughly 40). This is
an improvement over the best previously-known result by several orders of
magnitude, and it shows that spin-glass-like frustration can occur in
translationally-invariant quantum systems with a local dimension comparable to
the smallest-known non-translationally-invariant systems with similar
behaviour.
While previous constructions of such systems rely on standard models of
quantum computation, we construct a new model that is particularly well-suited
for encoding quantum computation into the ground state of a
translationally-invariant system. This allows us to shift the proof burden from
optimizing the Hamiltonian encoding a standard computational model to proving
universality of a simple model.
Previous techniques for encoding quantum computation into the ground state of
a local Hamiltonian allow only a linear sequence of gates, hence only a linear
(or nearly linear) path in the graph of all computational states. We extend
these techniques by allowing significantly more general paths, including
branching and cycles, thus enabling a highly efficient encoding of our
computational model. However, this requires more sophisticated techniques for
analysing the spectrum of the resulting Hamiltonian. To address this, we
introduce a framework of graphs with unitary edge labels. After relating our
Hamiltonian to the Laplacian of such a unitary labelled graph, we analyse its
spectrum by combining matrix analysis and spectral graph theory techniques.Comment: 69 page | The Complexity of Translationally-Invariant Spin Chains with Low Local
Dimension | the complexity of translationally-invariant spin chains with low local dimension | estimating translationally nearest neighbour qmaexp roughly orders glass frustration translationally comparable smallest translationally behaviour. constructions rely suited encoding translationally system. burden optimizing encoding proving universality model. encoding gates nearly states. extend allowing paths branching cycles enabling encoding model. sophisticated analysing hamiltonian. unitary labels. relating laplacian unitary labelled analyse combining | non_dup | [] |
83839326 | 10.1007/s00023-017-0611-0 | A large class of N=2 quantum field theories admits a BPS quiver description
and the study of their BPS spectra is then reduced to a representation theory
problem. In such theories the coupling to a line defect can be modelled by
framed quivers. The associated spectral problem characterises the line defect
completely. Framed BPS states can be thought of as BPS particles bound to the
defect. We identify the framed BPS degeneracies with certain enumerative
invariants associated with the moduli spaces of stable quiver representations.
We develop a formalism based on equivariant localization to compute explicitly
such BPS invariants, for a particular choice of stability condition. Our
framework gives a purely combinatorial solution of this problem. We detail our
formalism with several explicit examples.Comment: 67 pages, 17 figure | Quivers, Line Defects and Framed BPS Invariants | quivers, line defects and framed bps invariants | admits quiver problem. defect modelled framed quivers. characterises defect completely. framed thought defect. framed degeneracies enumerative invariants moduli quiver representations. formalism equivariant localization explicitly invariants condition. purely combinatorial problem. formalism pages | non_dup | [] |
73987698 | 10.1007/s00023-017-0612-z | We study the {\it quasi-classical limit} of a quantum system composed of
finitely many non-relativistic particles coupled to a quantized field in
Nelson-type models. We prove that, as the field becomes classical and the
corresponding degrees of freedom are traced out, the effective Hamiltonian of
the particles converges in resolvent sense to a self-adjoint Schr\"{o}dinger
operator with an additional potential, depending on the state of the field.
Moreover, we explicitly derive the expression of such a potential for a large
class of field states and show that, for certain special sequences of states,
the effective potential is trapping. In addition, we prove convergence of the
ground state energy of the full system to a suitable effective variational
problem involving the classical state of the field.Comment: minor revision, Ann. H. Poincar\'e in press, 41 pages, pdfLaTe | Effective Potentials Generated by Field Interaction in the
Quasi-Classical Limit | effective potentials generated by field interaction in the quasi-classical limit | quasi composed finitely relativistic quantized nelson models. freedom traced converges resolvent adjoint schr dinger field. explicitly derive trapping. variational involving minor revision ann. poincar pages pdflate | non_dup | [] |
42752536 | 10.1007/s00023-017-0616-8 | Let $\mathfrak{g}$ be a semisimple Lie algebra over $\mathbb{C}$. Let $\nu
\in \text{Aut}\, \mathfrak{g}$ be a diagram automorphism whose order divides $T
\in \mathbb{Z}_{\geq 1}$. We define cyclotomic $\mathfrak{g}$-opers over the
Riemann sphere $\mathbb{P}^1$ as gauge equivalence classes of
$\mathfrak{g}$-valued connections of a certain form, equivariant under actions
of the cyclic group $\mathbb{Z}/ T\mathbb{Z}$ on $\mathfrak{g}$ and
$\mathbb{P}^1$. It reduces to the usual notion of $\mathfrak{g}$-opers when $T
= 1$.
We also extend the notion of Miura $\mathfrak{g}$-opers to the cyclotomic
setting. To any cyclotomic Miura $\mathfrak{g}$-oper $\nabla$ we associate a
corresponding cyclotomic $\mathfrak{g}$-oper. Let $\nabla$ have residue at the
origin given by a $\nu$-invariant rational dominant coweight
$\check{\lambda}_0$ and be monodromy-free on a cover of $\mathbb{P}^1$. We
prove that the subset of all cyclotomic Miura $\mathfrak{g}$-opers associated
with the same cyclotomic $\mathfrak{g}$-oper as $\nabla$ is isomorphic to the
$\vartheta$-invariant subset of the full flag variety of the adjoint group $G$
of $\mathfrak{g}$, where the automorphism $\vartheta$ depends on $\nu$, $T$ and
$\check{\lambda}_0$. The big cell of the latter is isomorphic to $N^\vartheta$,
the $\vartheta$-invariant subgroup of the unipotent subgroup $N \subset G$,
which we identify with those cyclotomic Miura $\mathfrak{g}$-opers whose
residue at the origin is the same as that of $\nabla$. In particular, the
cyclotomic generation procedure recently introduced in [arXiv:1505.07582] is
interpreted as taking $\nabla$ to other cyclotomic Miura $\mathfrak{g}$-opers
corresponding to elements of $N^\vartheta$ associated with simple root
generators.
We motivate the introduction of cyclotomic $\mathfrak{g}$-opers by
formulating two conjectures which relate them to the cyclotomic Gaudin model of
[arXiv:1409.6937].Comment: 59 page | Cyclotomic Gaudin models, Miura opers and flag varieties | cyclotomic gaudin models, miura opers and flag varieties | mathfrak semisimple mathbb mathfrak automorphism divides mathbb cyclotomic mathfrak opers riemann sphere mathbb equivalence mathfrak valued connections equivariant cyclic mathbb mathbb mathfrak mathbb reduces usual notion mathfrak opers extend notion miura mathfrak opers cyclotomic setting. cyclotomic miura mathfrak oper nabla associate cyclotomic mathfrak oper. nabla residue rational coweight check lambda monodromy cover mathbb cyclotomic miura mathfrak opers cyclotomic mathfrak oper nabla isomorphic vartheta flag adjoint mathfrak automorphism vartheta check lambda isomorphic vartheta vartheta subgroup unipotent subgroup cyclotomic miura mathfrak opers residue nabla cyclotomic interpreted nabla cyclotomic miura mathfrak opers vartheta generators. motivate cyclotomic mathfrak opers formulating conjectures relate cyclotomic gaudin .comment | non_dup | [] |
73993252 | 10.1007/s00023-017-0618-6 | We prove a limiting eigenvalue distribution theorem (LEDT) for suitably
scaled eigenvalue clusters around the discrete negative eigenvalues of the
hydrogen atom Hamiltonian formed by the perturbation by a weak constant
magnetic field. We study the hydrogen atom Zeeman Hamiltonian $H_V(h,B) =
(1/2)( - i h {\mathbf \nabla} - {\mathbf A}(h))^2 - |x|^{-1}$, defined on $L^2
(R^3)$, in a constant magnetic field ${\mathbf B}(h) = {\mathbf \nabla} \times
{\mathbf A}(h)=(0,0,\epsilon(h)B)$ in the weak field limit $\epsilon(h)
\rightarrow 0$ as $h\rightarrow{0}$. We consider the Planck's parameter $h$
taking values along the sequence $h=1/(N+1)$, with $N=0,1,2,\ldots$, and
$N\rightarrow\infty$. We prove a semiclassical $N \rightarrow \infty$ LEDT of
the Szeg\"o-type for the scaled eigenvalue shifts and obtain both ({\bf i}) an
expression involving the regularized classical Kepler orbits with energy
$E=-1/2$ and ({\bf ii}) a weak limit measure that involves the component
$\ell_3$ of the angular momentum vector in the direction of the magnetic field.
This LEDT extends results of Szeg\"o-type for eigenvalue clusters for bounded
perturbations of the hydrogen atom to the Zeeman effect. The new aspect of this
work is that the perturbation involves the unbounded, first-order, partial
differential operator $w(h, B) = \frac{(\epsilon(h)B)^2}{8} (x_1^2 + x_2^2) -
\frac{ \epsilon(h)B}{2} hL_3 ,$ where the operator $hL_3$ is the third
component of the usual angular momentum operator and is the quantization of
$\ell_3$. The unbounded Zeeman perturbation is controlled using localization
properties of both the hydrogen atom coherent states $\Psi_{\alpha,N}$, and
their derivatives $L_3(h)\Psi_{\alpha,N}$, in the large quantum number regime
$N\rightarrow\infty$.Comment: 39 page | Semiclassical Szeg\"o limit of eigenvalue clusters for the hydrogen atom
Zeeman Hamiltonian | semiclassical szeg\"o limit of eigenvalue clusters for the hydrogen atom zeeman hamiltonian | limiting eigenvalue ledt suitably scaled eigenvalue eigenvalues atom perturbation field. atom zeeman mathbf nabla mathbf mathbf mathbf nabla mathbf epsilon epsilon rightarrow rightarrow planck ldots rightarrow infty semiclassical rightarrow infty ledt szeg scaled eigenvalue shifts involving regularized kepler orbits involves field. ledt extends szeg eigenvalue perturbations atom zeeman effect. aspect perturbation involves unbounded frac epsilon frac epsilon usual quantization unbounded zeeman perturbation localization atom coherent alpha derivatives alpha rightarrow infty .comment | non_dup | [] |
73402594 | 10.1007/s00023-017-0619-5 | Given a compact surface $\mathcal{M}$ with a smooth area form $\omega$, we
consider an open and dense subset of the set of smooth closed 1-forms on
$\mathcal{M}$ with isolated zeros which admit at least one saddle loop
homologous to zero and we prove that almost every element in the former induces
a mixing flow on each minimal component. Moreover, we provide an estimate of
the speed of the decay of correlations for smooth functions with compact
support on the complement of the set of singularities. This result is achieved
by proving a quantitative version for the case of finitely many singularities
of a theorem by Ulcigrai (ETDS, 2007), stating that any suspension flow with
one asymmetric logarithmic singularity over almost every interval exchange
transformation is mixing. In particular, the quantitative mixing estimate we
prove applies to asymmetric logarithmic suspension flows over rotations, which
were shown to be mixing by Sinai and Khanin.Comment: 34 pages, 4 figures. Revised version according to the referees'
suggestion | Quantitative mixing for locally Hamiltonian flows with saddle loops on
compact surfaces | quantitative mixing for locally hamiltonian flows with saddle loops on compact surfaces | mathcal omega dense mathcal zeros admit saddle homologous former induces component. complement singularities. proving finitely singularities ulcigrai etds stating suspension asymmetric logarithmic singularity mixing. applies asymmetric logarithmic suspension flows rotations sinai pages figures. revised referees suggestion | non_dup | [] |
83839185 | 10.1007/s00023-017-0621-y | We investigate the possibility of constructing exponentially localized
composite Wannier bases, or equivalently smooth periodic Bloch frames, for
3-dimensional time-reversal symmetric topological insulators, both of bosonic
and of fermionic type, so that the bases in question are also compatible with
time-reversal symmetry. This problem is translated in the study, of independent
interest, of homotopy classes of continuous, periodic, and time-reversal
symmetric families of unitary matrices. We identify three $\mathbb{Z}_2$-valued
complete invariants for these homotopy classes. When these invariants vanish,
we provide an algorithm which constructs a "multi-step" logarithm that is
employed to continuously deform the given family into a constant one,
identically equal to the identity matrix. This algorithm leads to a
constructive procedure to produce the composite Wannier bases mentioned above.Comment: 29 pages. Version 2: minor corrections of misprints, corrected proofs
of Theorems 2.4 and 2.9, added references. Accepted for publication in
Annales Henri Poicar\' | On the construction of Wannier functions in topological insulators: the
3D case | on the construction of wannier functions in topological insulators: the 3d case | constructing exponentially localized composite wannier bases equivalently bloch frames reversal topological insulators bosonic fermionic bases compatible reversal symmetry. translated homotopy reversal families unitary matrices. mathbb valued invariants homotopy classes. invariants vanish constructs logarithm continuously deform identically matrix. constructive composite wannier bases pages. minor misprints corrected proofs theorems references. publication annales henri poicar | non_dup | [] |
73359870 | 10.1007/s00023-017-0625-7 | We consider expansions of eigenvalues and eigenvectors of models of quantum
field theory. For a class of models known as generalized spin boson model we
prove the existence of asymptotic expansions of the ground state and the ground
state energy to arbitrary order. We need a mild but very natural infrared
assumption, which is weaker than the assumption usually needed for other
methods such as operator theoretic renormalization to be applicable. The result
complements previously shown analyticity properties.Comment: 49 page | On Asymptotic Expansions in Spin Boson Models | on asymptotic expansions in spin boson models | expansions eigenvalues eigenvectors theory. boson asymptotic expansions order. mild infrared weaker theoretic renormalization applicable. complements analyticity | non_dup | [] |
83837388 | 10.1007/s00023-017-0627-5 | We present a simple one-dimensional Ising-type spin system on which we define
a completely asymmetric Markovian single spin-flip dynamics. We study the
system at a very low, yet non-zero, temperature and we show that for empty
boundary conditions the Gibbs measure is stationary for such dynamics, while
introducing in a single site a $+$ condition the stationary measure changes
drastically, with macroscopical effects. We achieve this result defining an
absolutely convergent series expansion of the stationary measure around the
zero temperature system. Interesting combinatorial identities are involved in
the proofs | Effects of boundary conditions on irreversible dynamics | effects of boundary conditions on irreversible dynamics | ising asymmetric markovian flip dynamics. empty gibbs stationary introducing stationary drastically macroscopical effects. defining absolutely convergent stationary system. combinatorial identities proofs | non_dup | [] |
73414006 | 10.1007/s00023-017-0630-x | We give a topological classification of quantum walks on an infinite 1D
lattice, which obey one of the discrete symmetry groups of the tenfold way,
have a gap around some eigenvalues at symmetry protected points, and satisfy a
mild locality condition. No translation invariance is assumed. The
classification is parameterized by three indices, taking values in a group,
which is either trivial, the group of integers, or the group of integers modulo
2, depending on the type of symmetry. The classification is complete in the
sense that two walks have the same indices if and only if they can be connected
by a norm continuous path along which all the mentioned properties remain
valid. Of the three indices, two are related to the asymptotic behaviour far to
the right and far to the left, respectively. These are also stable under
compact perturbations. The third index is sensitive to those compact
perturbations which cannot be contracted to a trivial one. The results apply to
the Hamiltonian case as well. In this case all compact perturbations can be
contracted, so the third index is not defined. Our classification extends the
one known in the translation invariant case, where the asymptotic right and
left indices add up to zero, and the third one vanishes, leaving effectively
only one independent index. When two translationally invariant bulks with
distinct indices are joined, the left and right asymptotic indices of the
joined walk are thereby fixed, and there must be eigenvalues at $1$ or $-1$
(bulk-boundary correspondence). Their location is governed by the third index.
We also discuss how the theory applies to finite lattices, with suitable
homogeneity assumptions.Comment: 36 pages, 7 figure | The topological classification of one-dimensional symmetric quantum
walks | the topological classification of one-dimensional symmetric quantum walks | topological walks infinite obey tenfold eigenvalues protected satisfy mild locality condition. translation invariance assumed. parameterized indices trivial integers integers modulo symmetry. walks indices norm valid. indices asymptotic respectively. perturbations. perturbations contracted trivial one. well. perturbations contracted defined. extends translation asymptotic indices vanishes leaving effectively index. translationally bulks indices joined asymptotic indices joined walk thereby eigenvalues correspondence governed index. applies lattices homogeneity pages | non_dup | [] |
42639641 | 10.1007/s00023-017-0631-9 | The vacuum Einstein equations in 5+1 dimensions are shown to admit solutions
describing naked singularity formation in gravitational collapse from
nonsingular asymptotically locally flat initial data that contain no trapped
surface. We present a class of specific examples with topology
$\mathbb{R}^{3+1} \times S^2$. Thanks to the Kaluza-Klein dimensional
reduction, these examples are constructed by lifting continuously self-similar
solutions of the 4-dimensional Einstein-scalar field system with a negative
exponential potential. The latter solutions are obtained by solving a
3-dimensional autonomous system of first-order ordinary differential equations
with a combined analytic and numerical approach. Their existence provides a new
test-bed for weak cosmic censorship in higher-dimensional gravity. In addition,
we point out that a similar attempt of lifting Christodoulou's naked
singularity solutions of massless scalar fields fails to capture formation of
naked singularities in 4+1 dimensions, due to a diverging Kretschmann scalar in
the initial data.Comment: 34 pages, 5 figures; to match the published version which combines
this number and arXiv:1509.0795 | Examples of naked singularity formation in higher-dimensional
Einstein-vacuum spacetimes | examples of naked singularity formation in higher-dimensional einstein-vacuum spacetimes | einstein admit describing naked singularity gravitational collapse nonsingular asymptotically locally trapped surface. topology mathbb thanks kaluza klein lifting continuously einstein exponential potential. solving autonomous ordinary analytic approach. cosmic censorship gravity. attempt lifting christodoulou naked singularity massless fails capture naked singularities diverging kretschmann pages match combines | non_dup | [] |
78510635 | 10.1007/s00023-017-0633-7 | We show that a stationary solution of the Einstein-Maxwell equations which is
close to a non-degenerate Reissner-Nordstr\"om-de Sitter solution is in fact
equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the
non-linear stability of the Kerr-Newman-de Sitter family of black holes for
small angular momenta, recently established by the author, together with an
extension argument for Killing vector fields. Our black hole uniqueness result
only requires the solution to have high but finite regularity; in particular,
we do not make any analyticity assumptions.Comment: 10 pages, 1 figur | Uniqueness of Kerr-Newman-de Sitter black holes with small angular
momenta | uniqueness of kerr-newman-de sitter black holes with small angular momenta | stationary einstein maxwell degenerate reissner nordstr sitter slowly rotating kerr newman sitter solution. kerr newman sitter holes momenta argument killing fields. uniqueness regularity analyticity pages figur | non_dup | [] |
42711177 | 10.1007/s00023-017-0634-6 | Robertson-Walker spacetimes within a large class are geometrically extended
to larger cosmologies that include spacetime points with zero and negative
cosmological times. In the extended cosmologies, the big bang is lightlike, and
though singular, it inherits some geometric structure from the original
spacetime. Spacelike geodesics are continuous across the cosmological time zero
submanifold which is parameterized by the radius of Fermi space slices, i.e, by
the proper distances along spacelike geodesics from a comoving observer to the
big bang. The continuous extension of the metric, and the continuously
differentiable extension of the leading Fermi metric coefficient $g_{\tau\tau}$
of the observer, restrict the geometry of spacetime points with pre-big bang
cosmological time coordinates. In our extensions the big bang is two
dimensional in a certain sense, consistent with some findings in quantum
gravity.Comment: 48 pages, 2 figure | Pre-big bang geometric extensions of inflationary cosmologies | pre-big bang geometric extensions of inflationary cosmologies | robertson walker spacetimes geometrically cosmologies spacetime cosmological times. cosmologies bang lightlike singular inherits geometric spacetime. spacelike geodesics cosmological submanifold parameterized fermi slices proper distances spacelike geodesics comoving observer bang. continuously differentiable fermi observer restrict spacetime bang cosmological coordinates. extensions bang pages | non_dup | [] |
83839708 | 10.1007/s00023-017-0636-4 | We discuss the Bisognano-Wichmann property for local Poincar\'e covariant
nets of standard subspaces. We give a sufficient algebraic condition on the
covariant representation ensuring the Bisognano-Wichmann and Duality properties
without further assumptions on the net called modularity condition. It holds
for direct integrals of scalar massive and massless representations. We present
a class of massive modular covariant nets not satisfying the Bisognano-Wichmann
property. Furthermore, we give an outlook in the standard subspace setting on
the relation between the Bisognano-Wichmann property and the Split property.Comment: Final version. To appear in Annales Henri Poincar\' | The Bisognano-Wichmann property on nets of standard subspaces, some
sufficient conditions | the bisognano-wichmann property on nets of standard subspaces, some sufficient conditions | bisognano wichmann poincar covariant nets subspaces. algebraic covariant ensuring bisognano wichmann duality assumptions modularity condition. integrals massive massless representations. massive modular covariant nets satisfying bisognano wichmann property. outlook subspace bisognano wichmann split version. annales henri poincar | non_dup | [] |
84330246 | 10.1007/s00023-017-0638-2 | The main goal of this paper is to put on solid mathematical grounds the
so-called Non-Equilibrium Green's Function (NEGF) transport formalism for open
systems. In particular, we derive the Jauho-Meir-Wingreen formula for the
time-dependent current through an interacting sample coupled to non-interacting
leads. Our proof is non-perturbative and uses neither complex-time Keldysh
contours, nor Langreth rules of 'analytic continuation'. We also discuss other
technical identities (Langreth, Keldysh) involving various many body Green's
functions. Finally, we study the Dyson equation for the advanced/retarded
interacting Green's function and we rigorously construct its (irreducible)
self-energy, using the theory of Volterra operators.Comment: Annales Henri Poincar\'e 201 | A mathematical account of the NEGF formalism | a mathematical account of the negf formalism | goal mathematical grounds negf formalism systems. derive jauho meir wingreen interacting interacting leads. perturbative neither keldysh contours langreth analytic continuation identities langreth keldysh involving functions. dyson advanced retarded interacting rigorously irreducible volterra annales henri poincar | non_dup | [] |
24768577 | 10.1007/s00023-017-0639-1 | We prove that the asymptotic behavior of the recoupling coefficients of the
symmetric group is characterized by a quantum marginal problem -- namely, by
the existence of quantum states of three particles with given eigenvalues for
their reduced density operators. This generalizes Wigner's observation that the
semiclassical behavior of the 6j-symbols for SU(2) -- fundamental to the
quantum theory of angular momentum -- is governed by the existence of Euclidean
tetrahedra. As a corollary, we deduce solely from symmetry considerations the
strong subadditivity property of the von Neumann entropy. Lastly, we show that
the problem of characterizing the eigenvalues of partial sums of Hermitian
matrices arises as a special case of the quantum marginal problem. We establish
a corresponding relation between the recoupling coefficients of the unitary and
symmetric groups, generalizing a classical result of Littlewood and Murnaghan.Comment: 25 page | Recoupling coefficients and quantum entropies | recoupling coefficients and quantum entropies | asymptotic recoupling marginal eigenvalues operators. generalizes wigner semiclassical symbols governed euclidean tetrahedra. corollary deduce solely considerations subadditivity neumann entropy. lastly characterizing eigenvalues sums hermitian arises marginal problem. establish recoupling unitary generalizing littlewood | non_dup | [] |
93954644 | 10.1007/s00023-017-0640-8 | We consider non-ergodic magnetic random Sch\"odinger operators with a bounded
magnetic vector potential. We prove an optimal Wegner estimate valid at all
energies. The proof is an adaptation of the arguments from [Kle13], combined
with a recent quantitative unique continuation estimate for eigenfunctions of
elliptic operators from [BTV15]. This generalizes Klein's result to operators
with a bounded magnetic vector potential. Moreover, we study the dependence of
the Wegner-constant on the disorder parameter. In particular, we show that
above the model-dependent threshold $E_0(\infty) \in (0, \infty]$, it is
impossible that the Wegner-constant tends to zero if the disorder increases.
This result is new even for the standard (ergodic) Anderson Hamiltonian with
vanishing magnetic field | Wegner estimate and disorder dependence for alloy-type Hamiltonians with
bounded magnetic potential | wegner estimate and disorder dependence for alloy-type hamiltonians with bounded magnetic potential | ergodic odinger potential. wegner valid energies. adaptation arguments continuation eigenfunctions elliptic generalizes klein potential. wegner disorder parameter. infty infty impossible wegner tends disorder increases. ergodic anderson vanishing | non_dup | [] |
83847893 | 10.1007/s00023-017-0642-6 | Let $H_{P,\sigma}$ be the single-electron fiber Hamiltonians of the massless
Nelson model at total momentum $P$ and infrared cut-off $\sigma>0$. We
establish detailed regularity properties of the corresponding $n$-particle
ground state wave functions $f^n_{P,\sigma}$ as functions of $P$ and $\sigma$.
In particular, we show that \[ |\partial_{P^j}f^{n}_{P,\sigma}(k_1,\ldots,
k_n)|, \ \ |\partial_{P^j} \partial_{P^{j'}} f^{n}_{P,\sigma}(k_1,\ldots, k_n)|
\leq \frac{1}{\sqrt{n!}} \frac{(c\lambda_0)^n}{\sigma^{\delta_{\lambda_0}}}
\prod_{i=1}^n\frac{ \chi_{[\sigma,\kappa)}(k_i)}{|k_i|^{3/2}}, \] where $c$ is
a numerical constant, $\lambda_0\mapsto \delta_{\lambda_0}$ is a positive
function of the maximal admissible coupling constant which satisfies
$\lim_{\lambda_0\to 0}\delta_{\lambda_0}=0$ and $\chi_{[\sigma,\kappa)}$ is the
(approximate) characteristic function of the energy region between the infrared
cut-off $\sigma$ and the ultraviolet cut-off $\kappa$. While the analysis of
the first derivative is relatively straightforward, the second derivative
requires a new strategy. By solving a non-commutative recurrence relation we
derive a novel formula for $f^n_{P,\sigma}$ with improved infrared properties.
In this representation $\partial_{P^{j'}}\partial_{P^{j}}f^n_{P,\sigma}$ is
amenable to sharp estimates obtained by iterative analytic perturbation theory
in part II of this series of papers. The bounds stated above are instrumental
for scattering theory of two electrons in the Nelson model, as explained in
part I of this series.Comment: 45 pages, minor revision | Coulomb scattering in the massless Nelson model III. Ground state wave
functions and non-commutative recurrence relations | coulomb scattering in the massless nelson model iii. ground state wave functions and non-commutative recurrence relations | sigma fiber hamiltonians massless nelson infrared sigma establish regularity sigma sigma sigma ldots sigma ldots frac sqrt frac lambda sigma delta lambda prod frac sigma kappa lambda mapsto delta lambda maximal admissible satisfies lambda delta lambda sigma kappa approximate infrared sigma ultraviolet kappa straightforward strategy. solving commutative recurrence derive sigma infrared properties. sigma amenable sharp iterative analytic perturbation papers. bounds stated instrumental nelson pages minor revision | non_dup | [] |
83868274 | 10.1007/s00023-018-0644-z | The derivation of effective evolution equations is central to the study of
non-stationary quantum many-body sytems, and widely used in contexts such as
superconductivity, nuclear physics, Bose-Einstein condensation and quantum
chemistry. We reformulate the Dirac-Frenkel approximation principle in terms of
reduced density matrices, and apply it to fermionic and bosonic many-body
systems. We obtain the Bogoliubov-de-Gennes and Hartree-Fock-Bogoliubov
equations, respectively. While we do not prove quantitative error estimates,
our formulation does show that the approximation is optimal within the class of
quasifree states. Furthermore, we prove well-posedness of the
Bogoliubov-de-Gennes equations in energy space and discuss conserved
quantities.Comment: 46 pages, 1 figure; v2: simplified proof of conservation of particle
number, additional references; v3: minor clarification | The Dirac-Frenkel Principle for Reduced Density Matrices, and the
Bogoliubov-de-Gennes Equations | the dirac-frenkel principle for reduced density matrices, and the bogoliubov-de-gennes equations | derivation stationary sytems widely contexts superconductivity bose einstein condensation chemistry. reformulate dirac frenkel fermionic bosonic systems. bogoliubov gennes hartree fock bogoliubov respectively. formulation quasifree states. posedness bogoliubov gennes conserved pages simplified conservation minor clarification | non_dup | [] |
83862161 | 10.1007/s00023-018-0645-y | Motivated by studies of indirect measurements in quantum mechanics, we
investigate stochastic differential equations with a fixed point subject to an
additional infinitesimal repulsive perturbation. We conjecture, and prove for
an important class, that the solutions exhibit a universal behavior when time
is rescaled appropriately: by fine-tuning of the time scale with the
infinitesimal repulsive perturbation, the trajectories converge in a precise
sense to spiky trajectories that can be reconstructed from an auxiliary
time-homogeneous Poisson process. Our results are based on two main tools. The
first is a time change followed by an application of Skorokhod's lemma. We
prove an effective approximate version of this lemma of independent interest.
The second is an analysis of first passage times, which shows a deep interplay
between scale functions and invariant measures. We conclude with some
speculations of possible applications of the same techniques in other areas | Stochastic spikes and strong noise limits of stochastic differential
equations | stochastic spikes and strong noise limits of stochastic differential equations | motivated indirect mechanics stochastic infinitesimal repulsive perturbation. conjecture exhibit universal rescaled appropriately fine tuning infinitesimal repulsive perturbation trajectories converge precise spiky trajectories reconstructed auxiliary homogeneous poisson process. tools. skorokhod lemma. approximate interest. passage interplay measures. speculations | non_dup | [] |
84329790 | 10.1007/s00023-018-0648-8 | We prove exponential correlation decay in dispersing billiard flows on the
2-torus assuming finite horizon and lack of corner points. With applications
aimed at describing heat conduction, the highly singular initial measures are
concentrated here on 1-dimensional submanifolds (given by standard pairs) and
the observables are supposed to satisfy a generalized H\"older continuity
property. The result is based on the exponential correlation decay bound of
Baladi, Demers and Liverani obtained recentlyfor H\"older continuous
observables in these billiards. The model dependence of the bounds is also
discussed.Comment: 2 figure | Equidistribution for standard pairs in planar dispersing billiard flows | equidistribution for standard pairs in planar dispersing billiard flows | exponential dispersing billiard flows torus horizon corner points. aimed describing conduction singular concentrated submanifolds observables supposed satisfy older continuity property. exponential baladi demers liverani recentlyfor older observables billiards. bounds | non_dup | [] |
83870695 | 10.1007/s00023-018-0653-y | We reformulate Super Quantum Mechanics in the context of integral forms. This
framework allows to interpolate between different actions for the same theory,
connected by different choices of Picture Changing Operators (PCO). In this way
we retrieve component and superspace actions, and prove their equivalence. The
PCO are closed integral forms, and can be interpreted as super Poincar\'e duals
of bosonic submanifolds embedded into a supermanifold.. We use them to
construct Lagrangians that are top integral forms, and therefore can be
integrated on the whole supermanifold. The $D=1, ~N=1$ and the $D=1,~ N=2$
cases are studied, in a flat and in a curved supermanifold. In this formalism
we also consider coupling with gauge fields, Hilbert space of quantum states
and observables.Comment: 41 pages, no figures. Use birkjour.cls. Minor misprints, moved
appendix A and B in the main text. Version to be published in Annales H.
Poincar\' | Super Quantum Mechanics in the Integral Form Formalism | super quantum mechanics in the integral form formalism | reformulate super mechanics forms. interpolate choices picture changing retrieve superspace equivalence. interpreted super poincar duals bosonic submanifolds embedded supermanifold.. lagrangians supermanifold. curved supermanifold. formalism hilbert pages figures. birkjour.cls. minor misprints moved text. annales poincar | non_dup | [] |
78512496 | 10.1007/s00023-018-0654-x | We investigate spectral properties of a Hermitised random matrix product
which, contrary to previous product ensembles, allows for eigenvalues on the
full real line. We prove that the eigenvalues form a bi-orthogonal ensemble,
which reduces asymptotically to the Hermite Muttalib-Borodin ensemble. Explicit
expressions for the bi-orthogonal functions as well as the correlation kernel
are provided. Scaling the latter near the origin gives a limiting kernel
involving Meijer G-functions, and the functional form of the global density is
calculated. As a part of this study, we introduce a new matrix transformation
which maps the space of polynomial ensembles onto itself. This matrix
transformation is closely related to the so-called hyperbolic
Harish-Chandra-Itzykson-Zuber integral.Comment: 33 pages. To appear in Ann. Henri Poincar | Matrix product ensembles of Hermite-type and the hyperbolic
Harish-Chandra-Itzykson-Zuber integral | matrix product ensembles of hermite-type and the hyperbolic harish-chandra-itzykson-zuber integral | hermitised contrary ensembles eigenvalues line. eigenvalues orthogonal ensemble reduces asymptotically hermite muttalib borodin ensemble. expressions orthogonal kernel provided. limiting kernel involving meijer calculated. ensembles itself. closely hyperbolic harish chandra itzykson zuber pages. ann. henri poincar | non_dup | [] |
73956997 | 10.1007/s00023-018-0656-8 | A theory of intermittency differentiation is developed for a general class of
1D Infinitely Divisible Multiplicative Chaos measures. The intermittency
invariance of the underlying infinitely divisible field is established and
utilized to derive a Feynman-Kac equation for the distribution of the total
mass of the limit measure by considering a stochastic flow in intermittency.
The resulting equation prescribes the rule of intermittency differentiation for
a general functional of the total mass and determines the distribution of the
total mass and its dependence structure to the first order in intermittency. A
class of non-local functionals of the limit measure extending the total mass is
introduced and shown to be invariant under intermittency differentiation making
the computation of the full high temperature expansion of the total mass
distribution possible in principle. For application, positive integer moments
and covariance structure of the total mass are considered in detail.Comment: 38 page | A Theory of Intermittency Differentiation of 1D Infinitely Divisible
Multiplicative Chaos Measures | a theory of intermittency differentiation of 1d infinitely divisible multiplicative chaos measures | intermittency infinitely divisible multiplicative chaos measures. intermittency invariance infinitely divisible utilized derive feynman stochastic intermittency. prescribes intermittency determines intermittency. functionals extending intermittency principle. integer moments covariance | non_dup | [] |
86416042 | 10.1007/s00023-018-0657-7 | Floquet topological insulators describe independent electrons on a lattice
driven out of equilibrium by a time-periodic Hamiltonian, beyond the usual
adiabatic approximation. In dimension two such systems are characterized by
integer-valued topological indices associated to the unitary propagator,
alternatively in the bulk or at the edge of a sample. In this paper we give new
definitions of the two indices, relying neither on translation invariance nor
on averaging, and show that they are equal. In particular weak disorder and
defects are intrinsically taken into account. Finally indices can be defined
when two driven sample are placed next to one another either in space or in
time, and then shown to be equal. The edge index is interpreted as a quantized
pumping occurring at the interface with an effective vacuum.Comment: 28 pages, 5 figures Minor changes, update and addition of some
references To appear in Annales Henri Poincar\' | Bulk-Edge correspondence for two-dimensional Floquet topological
insulators | bulk-edge correspondence for two-dimensional floquet topological insulators | floquet topological insulators usual adiabatic approximation. integer valued topological indices unitary propagator alternatively sample. definitions indices relying neither translation invariance averaging equal. disorder defects intrinsically account. indices placed equal. interpreted quantized pumping occurring pages minor update annales henri poincar | non_dup | [] |
84331467 | 10.1007/s00023-018-0659-5 | In this paper we consider the Witten Laplacian on 0-forms and give sufficient
conditions under which the Witten Laplacian admits a compact resolvent. These
conditions are imposed on the potential itself, involving the control of high
order derivatives by lower ones, as well as the control of the positive
eigenvalues of the Hessian matrix. This compactness criterion for resolvent is
inspired by the one for the Fokker-Planck operator. Our method relies on the
nilpotent group techniques developed by Helffer-Nourrigat [Hypoellipticit\'e
maximale pour des op\'erateurs polyn\^omes de champs de vecteurs, 1985].Comment: 25page | Compactness of the resolvent for the Witten Laplacian | compactness of the resolvent for the witten laplacian | witten laplacian witten laplacian admits resolvent. imposed involving derivatives eigenvalues hessian matrix. compactness criterion resolvent inspired fokker planck operator. relies nilpotent helffer nourrigat hypoellipticit maximale pour erateurs polyn omes champs vecteurs .comment | non_dup | [] |
86421708 | 10.1007/s00023-018-0660-z | In this work, we investigate the possibility of compressing a quantum system
to one of smaller dimension in a way that preserves the measurement statistics
of a given set of observables. In this process, we allow for an arbitrary
amount of classical side information. We find that the latter can be bounded,
which implies that the minimal compression dimension is stable in the sense
that it cannot be decreased by allowing for small errors. Various bounds on the
minimal compression dimension are proven and an SDP-based algorithm for its
computation is provided. The results are based on two independent approaches:
an operator algebraic method using a fixed point result by Arveson and an
algebro-geometric method that relies on irreducible polynomials and B\'ezout's
theorem. The latter approach allows lifting the results from the single copy
level to the case of multiple copies and from completely positive to merely
positive maps.Comment: 40 pages. Minor clarifications in Section 9.2 and Section 7. | Quantum compression relative to a set of measurements | quantum compression relative to a set of measurements | compressing preserves observables. information. compression allowing errors. bounds compression proven provided. algebraic arveson algebro geometric relies irreducible polynomials ezout theorem. lifting copy copies merely pages. minor clarifications | non_dup | [] |
84330722 | 10.1007/s00023-018-0661-y | This paper deals with the study of the two-dimensional Dirac operatorwith
infinite mass boundary condition in a sector. We investigate the question
ofself-adjointness depending on the aperture of the sector: when the sector is
convexit is self-adjoint on a usual Sobolev space whereas when the sector is
non-convexit has a family of self-adjoint extensions parametrized by a complex
number of theunit circle. As a byproduct of this analysis we are able to give
self-adjointnessresults on polygones. We also discuss the question of
distinguished self-adjointextensions and study basic spectral properties of the
operator in the sector | Self-Adjointness of Dirac Operators with Infinite Mass Boundary
Conditions in Sectors | self-adjointness of dirac operators with infinite mass boundary conditions in sectors | deals dirac operatorwith infinite sector. ofself adjointness aperture convexit adjoint usual sobolev convexit adjoint extensions parametrized theunit circle. byproduct adjointnessresults polygones. distinguished adjointextensions | non_dup | [] |
93943778 | 10.1007/s00023-018-0662-x | 2D quantum gravity is the idea that a set of discretized surfaces (called
map, a graph on a surface), equipped with a graph measure, converges in the
large size limit (large number of faces) to a conformal field theory (CFT), and
in the simplest case to the simplest CFT known as pure gravity, also known as
the gravity dressed (3,2) minimal model. Here we consider the set of planar
Strebel graphs (planar trivalent metric graphs) with fixed perimeter faces,
with the measure product of Lebesgue measure of all edge lengths, submitted to
the perimeter constraints. We prove that expectation values of a large class of
observables indeed converge towards the CFT amplitudes of the (3,2) minimal
model.Comment: 35 pages, 6 figures, misprints corrected, presentation of appendix A
modifie | Large Strebel graphs and $(3,2)$ Liouville CFT | large strebel graphs and $(3,2)$ liouville cft | discretized equipped converges faces conformal simplest simplest dressed model. planar strebel planar trivalent perimeter faces lebesgue lengths submitted perimeter constraints. expectation observables converge amplitudes pages misprints corrected presentation modifie | non_dup | [] |
86417919 | 10.1007/s00023-018-0664-8 | The concept of balance between two state preserving quantum Markov semigroups
on von Neumann algebras is introduced and studied as an extension of conditions
appearing in the theory of quantum detailed balance. This is partly motivated
by the theory of joinings. Balance is defined in terms of certain correlated
states (couplings), with entangled states as a specific case. Basic properties
of balance are derived and the connection to correspondences in the sense of
Connes is discussed. Some applications and possible applications, including to
non-equilibrium statistical mechanics, are briefly explored.Comment: v1: 40 pages. v2: Corrections and small additions made, 41 page | Balance between quantum Markov semigroups | balance between quantum markov semigroups | balance preserving markov semigroups neumann algebras appearing balance. partly motivated joinings. balance couplings entangled case. balance connection correspondences connes discussed. mechanics briefly pages. additions | non_dup | [] |
73357975 | 10.1007/s00023-018-0670-x | We show that Araki and Masuda's weighted non-commutative vector valued
$L_p$-spaces [Araki \& Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)]
correspond to an algebraic generalization of the sandwiched R\'enyi divergences
with parameter $\alpha = \frac{p}{2}$. Using complex interpolation theory, we
prove various fundamental properties of these divergences in the setup of von
Neumann algebras, including a data-processing inequality and monotonicity in
$\alpha$. We thereby also give new proofs for the corresponding
finite-dimensional properties. We discuss the limiting cases $\alpha\to
\{\frac{1}{2},1,\infty\}$ leading to minus the logarithm of Uhlmann's fidelity,
Umegaki's relative entropy, and the max-relative entropy, respectively. As a
contribution that might be of independent interest, we derive a Riesz-Thorin
theorem for Araki-Masuda $L_p$-spaces and an Araki-Lieb-Thirring inequality for
states on von Neumann algebras.Comment: v2: 20 pages, published versio | R\'enyi divergences as weighted non-commutative vector valued
$L_p$-spaces | r\'enyi divergences as weighted non-commutative vector valued $l_p$-spaces | araki masuda weighted commutative valued araki masuda publ. res. inst. math. sci. algebraic generalization sandwiched enyi divergences alpha frac interpolation divergences setup neumann algebras inequality monotonicity alpha thereby proofs properties. limiting alpha frac infty minus logarithm uhlmann fidelity umegaki respectively. derive riesz thorin araki masuda araki lieb thirring inequality neumann pages versio | non_dup | [] |
73987567 | 10.1007/s00023-018-0671-9 | We consider the entanglement entropy for a spacetime region and its spacelike
complement in the framework of algebraic quantum field theory. For a M\"obius
covariant local net satisfying a certain nuclearity property, we consider the
von Neumann entropy for type I factors between local algebras and introduce an
entropic quantity. Then we implement a cutoff on this quantity with respect to
the conformal Hamiltonian and show that it remains finite as the distance of
two intervals tends to zero. We compare our definition to others in the
literature.Comment: 23 page | Towards entanglement entropy with UV cutoff in conformal nets | towards entanglement entropy with uv cutoff in conformal nets | entanglement spacetime spacelike complement algebraic theory. obius covariant satisfying nuclearity neumann algebras entropic quantity. implement cutoff quantity conformal intervals tends zero. | non_dup | [] |
141530837 | 10.1007/s00023-018-0673-7 | We consider effective models of condensation where the condensation occurs as
time t goes to infinity. We provide natural conditions under which the build-up
of the condensate occurs on a spatial scale of 1/t and has the universal form
of a Gamma density. The exponential parameter of this density is determined
only by the equation and the total mass of the condensate, while the power law
parameter may in addition depend on the decay properties of the initial
condition near the condensation point. We apply our results to some examples,
including simple models of Bose-Einstein condensation | The shape of the emerging condensate in effective models of condensation | the shape of the emerging condensate in effective models of condensation | condensation condensation goes infinity. build condensate universal gamma density. exponential condensate condensation point. bose einstein condensation | non_dup | [] |
93955771 | 10.1007/s00023-018-0674-6 | We consider the statistical motion of a convex rigid body in a gas of N
smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid
body is much bigger and heavier, it undergoes a lot of collisions leading to
small deflections. We prove that its velocity is described, in a suitable
limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on
Lanford's arguments [17] together with the pruning procedure from [3] to reach
diffusive times, much larger than the mean free time. Furthermore, we need to
introduce a modified dynamics to avoid pathological collisions of atoms with
the rigid body: these collisions, due to the geometry of the rigid body,
require developing a new type of trajectory analysis | Derivation of an ornstein-uhlenbeck process for a massive particle in a
rarified gas of particles | derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles | convex rigid spherical thermodynamic equilibrium. rigid bigger heavier undergoes collisions deflections. ornstein uhlenbeck process. relies lanford arguments pruning diffusive time. avoid pathological collisions rigid collisions rigid trajectory | non_dup | [] |
129356946 | 10.1007/s00023-018-0675-5 | We prove a global limiting absorption principle on the entire real line for
free, massless Dirac operators $H_0 = \alpha \cdot (-i \nabla)$ for all space
dimensions $n \in \mathbb{N}$, $n \geq 2$. This is a new result for all
dimensions other than three, in particular, it applies to the two-dimensional
case which is known to be of some relevance in applications to graphene.
We also prove an essential self-adjointness result for first-order
matrix-valued differential operators with Lipschitz coefficients.Comment: 22 page | On the Global Limiting Absorption Principle for Massless Dirac Operators | on the global limiting absorption principle for massless dirac operators | limiting massless dirac alpha cdot nabla mathbb applies relevance graphene. adjointness valued lipschitz | non_dup | [] |
141536919 | 10.1007/s00023-018-0676-4 | We give a simple and direct treatment of the strong convergence of quantum
random walks to quantum stochastic operator cocycles, via the semigroup
decomposition of such cocycles. Our approach also delivers convergence of the
pointwise product of quantum random walks to the quantum stochastic Trotter
product of the respective limit cocycles, thereby revealing the algebraic
structure of the limiting procedure. The repeated quantum interactions model is
shown to fit nicely into the convergence scheme described.Comment: 29 pages. To appear in the journal Annales Henri Poincare. Revisions
made in v2; typos corrected in v3; final correction in v | Strong convergence of quantum random walks via semigroup decomposition | strong convergence of quantum random walks via semigroup decomposition | walks stochastic cocycles semigroup decomposition cocycles. delivers pointwise walks stochastic trotter respective cocycles thereby revealing algebraic limiting procedure. repeated nicely pages. annales henri poincare. revisions typos corrected | non_dup | [] |
83862279 | 10.1007/s00023-018-0679-1 | We analyze Landauer's principle for repeated interaction systems consisting
of a reference quantum system $\mathcal{S}$ in contact with an environment
$\mathcal{E}$ which is a chain of independent quantum probes. The system
$\mathcal{S}$ interacts with each probe sequentially, for a given duration, and
the Landauer principle relates the energy variation of $\mathcal{E}$ and the
decrease of entropy of $\mathcal{S}$ by the entropy production of the dynamical
process. We consider refinements of the Landauer bound at the level of the full
statistics (FS) associated to a two-time measurement protocol of, essentially,
the energy of $\mathcal{E}$. The emphasis is put on the adiabatic regime where
the environment, consisting of $T \gg 1$ probes, displays variations of order
$T^{-1}$ between the successive probes, and the measurements take place
initially and after $T$ interactions. We prove a large deviation principle and
a central limit theorem as $T \to \infty$ for the classical random variable
describing the entropy production of the process, with respect to the FS
measure. In a special case, related to a detailed balance condition, we obtain
an explicit limiting distribution of this random variable without rescaling. At
the technical level, we obtain a non-unitary adiabatic theorem generalizing
that of [Commun. Math. Phys. (2017) 349: 285] and analyze the spectrum of
complex deformations of families of irreducible completely positive
trace-preserving maps.Comment: 48 pages, 4 figures; fixed typos, made cosmetic changes, and added
Lemma 5.5. To appear in Annales Henri Poincar\' | Landauer's Principle for Trajectories of Repeated Interaction Systems | landauer's principle for trajectories of repeated interaction systems | analyze landauer repeated consisting mathcal mathcal probes. mathcal interacts sequentially landauer relates mathcal mathcal process. refinements landauer essentially mathcal emphasis adiabatic consisting probes displays successive probes initially interactions. infty describing measure. balance limiting rescaling. unitary adiabatic generalizing commun. math. phys. analyze deformations families irreducible trace preserving pages typos cosmetic annales henri poincar | non_dup | [] |
86418455 | 10.1007/s00023-018-0682-6 | We study a question which has natural interpretations in both quantum
mechanics and in geometry. Let $V_1,..., V_n$ be complex vector spaces of
dimension $d_1,...,d_n$ and let $G= SL_{d_1} \times \dots \times SL_{d_n}$.
Geometrically, we ask given $(d_1,...,d_n)$, when is the geometric invariant
theory quotient $\mathbb{P}(V_1 \otimes \dots \otimes V_n)// G$ non-empty? This
is equivalent to the quantum mechanical question of whether the multipart
quantum system with Hilbert space $V_1\otimes \dots \otimes V_n$ has a locally
maximally entangled state, i.e. a state such that the density matrix for each
elementary subsystem is a multiple of the identity. We show that the answer to
this question is yes if and only if $R(d_1,...,d_n)\geqslant 0$ where \[
R(d_1,...,d_n) = \prod_i d_i +\sum_{k=1}^n (-1)^k \sum_{1\leq i_1<\dotsb
<i_k\leq n} (\gcd(d_{i_1},\dotsc ,d_{i_k}) )^{2}. \] We also provide a simple
recursive algorithm which determines the answer to the question, and we compute
the dimension of the resulting quotient in the non-empty cases.Comment: Improved the exposition and streamlined some proofs using results of
Littelmann and Sato-Kimur | Existence of locally maximally entangled quantum states via geometric
invariant theory | existence of locally maximally entangled quantum states via geometric invariant theory | interpretations mechanics geometry. dots geometrically geometric quotient mathbb otimes dots otimes empty multipart hilbert otimes dots otimes locally maximally entangled i.e. elementary subsystem identity. answer geqslant prod dotsb dotsc recursive determines answer quotient empty exposition streamlined proofs littelmann sato kimur | non_dup | [] |
73382236 | 10.1007/s00023-018-0683-5 | We propose an extension of the sandwiched R\'enyi relative $\alpha$-entropy
to normal positive functionals on arbitrary von Neumann algebras, for the
values $\alpha>1$. For this, we use Kosaki's definition of noncommutative
$L_p$-spaces with respect to a state. Some properties of these extensions are
proved, in particular the limit values for $\alpha\to 1,\infty$ and data
processing inequality with respect to positive normal unital maps. This implies
that the Araki relative entropy satisfies DPI with respect to such maps,
extending the results of [A. M\"uller-Hermes and D. Reeb. Annales Henri
Poincar\'e 18, 1777-1788, 2017] to arbitrary von Neumann algebras. It is also
shown that equality in data processing inequality characterizes sufficiency
(reversibility) of quantum channels.Comment: 29 pages, minor changes and corrections. Comments welcom | R\'enyi relative entropies and noncommutative $L_p$-spaces | r\'enyi relative entropies and noncommutative $l_p$-spaces | propose sandwiched enyi alpha functionals neumann algebras alpha kosaki noncommutative state. extensions proved alpha infty inequality unital maps. araki satisfies extending uller hermes reeb. annales henri poincar neumann algebras. equality inequality characterizes sufficiency reversibility pages minor corrections. comments welcom | non_dup | [] |
73990356 | 10.1007/s00023-018-0686-2 | We establish the existence of $1$-parameter families of $\epsilon$-dependent
solutions to the Einstein-Euler equations with a positive cosmological constant
$\Lambda >0$ and a linear equation of state $p=\epsilon^2 K \rho$, $0<K\leq
1/3$, for the parameter values $0<\epsilon < \epsilon_0$. These solutions exist
globally to the future, converge as $\epsilon \searrow 0$ to solutions of the
cosmological Poison-Euler equations of Newtonian gravity, and are inhomogeneous
non-linear perturbations of FLRW fluid solutions.Comment: 58 pages. Agrees with published version. Note the title has been
changed. Old title "Cosmological Newtonian limits on long time scales"; New
title "Newtonian Limits of Isolated Cosmological Systems on Long Time Scales | Newtonian Limits of Isolated Cosmological Systems on Long Time Scales | newtonian limits of isolated cosmological systems on long time scales | establish families epsilon einstein euler cosmological lambda epsilon epsilon epsilon globally converge epsilon searrow cosmological poison euler newtonian inhomogeneous perturbations flrw pages. agrees version. title changed. title cosmological newtonian title newtonian cosmological | non_dup | [] |
146473009 | 10.1007/s00023-018-0687-1 | We analyze quantum field theories on spacetimes $M$ with timelike boundary
from a model-independent perspective. We construct an adjunction which
describes a universal extension to the whole spacetime $M$ of theories defined
only on the interior $\mathrm{int}M$. The unit of this adjunction is a natural
isomorphism, which implies that our universal extension satisfies Kay's
F-locality property. Our main result is the following characterization theorem:
Every quantum field theory on $M$ that is additive from the interior (i.e.\
generated by observables localized in the interior) admits a presentation by a
quantum field theory on the interior $\mathrm{int}M$ and an ideal of its
universal extension that is trivial on the interior. We shall illustrate our
constructions by applying them to the free Klein-Gordon field.Comment: 27 pages, final version published in Annales Henri Poincar\' | Algebraic quantum field theory on spacetimes with timelike boundary | algebraic quantum field theory on spacetimes with timelike boundary | analyze spacetimes timelike perspective. adjunction describes universal spacetime interior mathrm adjunction isomorphism universal satisfies locality property. additive interior i.e. observables localized interior admits presentation interior mathrm ideal universal trivial interior. illustrate constructions klein gordon pages annales henri poincar | non_dup | [] |
29552219 | 10.1007/s00023-018-0689-z | We study the eleven dimensional supergravity equations which describe a low
energy approximation to string theories and are related to M-theory under the
AdS/CFT correspondence. These equations take the form of a non-linear
differential system, on $\mathbb{B}^7\times\mathbb{S}^4$ with the
characteristic degeneracy at the boundary of an edge system, associated to the
fibration with fiber $\mathbb{S}^4.$ We compute the indicial roots of the
linearized system from the Hodge decomposition of the 4-sphere following the
work of Kantor, then using the edge calculus and scattering theory we prove
that the moduli space of solutions, near the Freund--Rubin states, is
parametrized by three pairs of data on the bounding 6-sphere.Comment: 48 pages, 1 figure. To appear in Annales Henri Poincar | The eleven dimensional supergravity equations on edge manifolds | the eleven dimensional supergravity equations on edge manifolds | eleven supergravity correspondence. mathbb mathbb degeneracy fibration fiber mathbb indicial roots linearized hodge decomposition sphere kantor calculus moduli freund rubin parametrized bounding pages figure. annales henri poincar | non_dup | [] |
129357790 | 10.1007/s00023-018-0691-5 | Product matrix processes are multi-level point processes formed by the
singular values of random matrix products. In this paper we study such
processes where the products of up to $m$ complex random matrices are no longer
independent, by introducing a coupling term and potentials for each product. We
show that such a process still forms a multi-level determinantal point
processes, and give formulae for the relevant correlation functions in terms of
the corresponding kernels.
For a special choice of potential, leading to a Gaussian coupling between the
$m$th matrix and the product of all previous $m-1$ matrices, we derive a
contour integral representation for the correlation kernels suitable for an
asymptotic analysis of large matrix size $n$. Here, the correlations between
the first $m-1$ levels equal that of the product of $m-1$ independent matrices,
whereas all correlations with the $m$th level are modified. In the hard edge
scaling limit at the origin of the spectra of all products we find three
different asymptotic regimes. The first regime corresponding to weak coupling
agrees with the multi-level process for the product of $m$ independent complex
Gaussian matrices for all levels, including the $m$-th. This process was
introduced by one of the authors and can be understood as a multi-level
extension of the Meijer $G$-kernel introduced by Kuijlaars and Zhang. In the
second asymptotic regime at strong coupling the point process on level $m$
collapses onto level $m-1$, thus leading to the process of $m-1$ independent
matrices. Finally, in an intermediate regime where the coupling is proportional
to $n^{\frac12}$, we obtain a family of parameter dependent kernels,
interpolating between the limiting processes in the weak and strong coupling
regime. These findings generalise previous results of the authors and their
coworkers for $m=2$.Comment: 50 pages; v2 grant number added; v3 Remark and Proposition added,
typo corrected, version to appear in AH | Product matrix processes for coupled multi-matrix models and their hard
edge scaling limits | product matrix processes for coupled multi-matrix models and their hard edge scaling limits | singular products. introducing potentials product. determinantal formulae kernels. derive contour kernels asymptotic modified. asymptotic regimes. agrees understood meijer kernel kuijlaars zhang. asymptotic collapses matrices. frac kernels interpolating limiting regime. generalise coworkers .comment pages remark typo corrected | non_dup | [] |
84093610 | 10.1007/s00023-018-0692-4 | We study the asymptotic speed of traveling fronts of the scalar reaction
diffusion for positive reaction terms and with a diffusion coefficient
depending nonlinearly on the concentration and on its gradient. We restrict our
study to diffusion coefficients of the form $D(u,u_x) = m u^{m-1} u_x^{m(p-2)}$
for which existence and convergence to traveling fronts has been established.
We formulate a variational principle for the asymptotic speed of the fronts.
Upper and lower bounds for the speed valid for any $m\ge0, p\ge 1$ are
constructed. When $m=1, p=2$ the problem reduces to the constant diffusion
problem and the bounds correspond to the classic Zeldovich Frank-Kamenetskii
lower bound and the Aronson-Weinberger upper bound respectively. In the special
case $m(p-1) = 1$ a local lower bound can be constructed which coincides with
the aforementioned upper bound. The speed in this case is completely determined
in agreement with recent results.Comment: 11 page | Variational characterization of the speed of reaction diffusion fronts
for gradient dependent diffusion | variational characterization of the speed of reaction diffusion fronts for gradient dependent diffusion | asymptotic traveling fronts nonlinearly gradient. restrict traveling fronts established. formulate variational asymptotic fronts. bounds valid constructed. reduces bounds classic zeldovich frank kamenetskii aronson weinberger respectively. coincides aforementioned bound. | non_dup | [] |
93958350 | 10.1007/s00023-018-0693-3 | We consider ferromagnetic long-range Ising models which display phase
transitions. They are long-range one-dimensional Ising ferromagnets, in which
the interaction is given by $J_{x,y} = J(|x-y|)\equiv
\frac{1}{|x-y|^{2-\alpha}}$ with $\alpha \in [0, 1)$, in particular, $J(1)=1$.
For this class of models one way in which one can prove the phase transition is
via a kind of Peierls contour argument, using the adaptation of the
Fr\"ohlich-Spencer contours for $\alpha \neq 0$, proposed by Cassandro,
Ferrari, Merola and Presutti. As proved by Fr\"ohlich and Spencer for
$\alpha=0$ and conjectured by Cassandro et al for the region they could treat,
$\alpha \in (0,\alpha_{+})$ for $\alpha_+=\log(3)/\log(2)-1$, although in the
literature dealing with contour methods for these models it is generally
assumed that $J(1)\gg1$, we can show that this condition can be removed in the
contour analysis. In addition, combining our theorem with a recent result of
Littin and Picco we prove the persistence of the contour proof of the phase
transition for any $\alpha \in [0,1)$. Moreover, we show that when we add a
magnetic field decaying to zero, given by $h_x= h_*\cdot(1+|x|)^{-\gamma}$ and
$\gamma >\max\{1-\alpha, 1-\alpha^* \}$ where $\alpha^*\approx 0.2714$, the
transition still persists.Comment: 13 page | Contour methods for long-range Ising models: weakening nearest-neighbor
interactions and adding decaying fields | contour methods for long-range ising models: weakening nearest-neighbor interactions and adding decaying fields | ferromagnetic ising display transitions. ising ferromagnets equiv frac alpha alpha kind peierls contour argument adaptation ohlich spencer contours alpha cassandro ferrari merola presutti. proved ohlich spencer alpha conjectured cassandro treat alpha alpha alpha dealing contour removed contour analysis. combining littin picco persistence contour alpha decaying cdot gamma gamma alpha alpha alpha approx | non_dup | [] |