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Nilpotence Varieties Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-16 Richard Eager, Ingmar Saberi, Johannes Walcher
We consider algebraic varieties canonically associated with any Lie superalgebra, and study them in detail for super-Poincaré algebras of physical interest. They are the locus of nilpotent elements in (the projectivized parity reversal of) the odd part of the algebra. Most of these varieties have appeared in various guises in previous literature, but we study them systematically here, from a new perspective:
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Schrödinger Operators Generated by Locally Constant Functions on the Fibonacci Subshift Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-16 David Damanik, Licheng Fang, Hyunkyu Jun
We investigate the spectral properties of discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the elements of the Fibonacci subshift with a locally constant function. The fundamental trace map formalism for this model is presented and related to its spectral features via an extension of a multitude of works on the classical model, where the sampling function
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On the Asymptotic Dynamics of 2-D Magnetic Quantum Systems Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-08 Esteban Cárdenas, Dirk Hundertmark, Edgardo Stockmeyer, Semjon Vugalter
In this work, we provide results on the long-time localization in space (dynamical localization) of certain two-dimensional magnetic quantum systems. The underlying Hamiltonian may have the form \(H=H_0+W\), where \(H_0\) is rotationally symmetric and has dense point spectrum and W is a perturbation that breaks the rotational symmetry. In the latter case, we also give estimates for the growth of the
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Fermionic Topological Order on Generic Triangulations Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-08 Emil Prodan
Consider a finite triangulation of a surface M of genus g and assume that spin-less fermions populate the edges of the triangulation. The quantum dynamics of such particles takes place inside the algebra of canonical anti-commutation relations (CAR). Following Kitaev’s work on toric models, we identify a sub-algebra of CAR generated by elements associated to the triangles and vertices of the triangulation
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Inverse scattering for reflectionless Schrödinger operators with integrable potentials and generalized soliton solutions for the KdV equation Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-07 Rostyslav Hryniv, Bohdan Melnyk, Yaroslav Mykytyuk
We give a complete characterization of the reflectionless Schrödinger operators on the line with integrable potentials, solve the inverse scattering problem of reconstructing such potentials from the eigenvalues and norming constants, and derive the corresponding generalized soliton solutions of the Korteweg–de Vries equation.
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Asymptotic Behavior of a Sequence of Conditional Probability Distributions and the Canonical Ensemble Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-07 Yu-Chen Cheng, Hong Qian, Yizhe Zhu
The probability distribution of a function of a subsystem conditioned on the value of the function of the whole, in the limit when the ratio of their values goes to zero, has a limit law: It equals the unconditioned marginal probability distribution weighted by an exponential factor whose exponent is uniquely determined by the condition. We apply this theorem to explain the canonical equilibrium ensemble
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Characterizing Topological Order with Matrix Product Operators Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-07 Mehmet Burak Şahinoğlu, Dominic Williamson, Nick Bultinck, Michaël Mariën, Jutho Haegeman, Norbert Schuch, Frank Verstraete
One of the most striking features of gapped quantum phases that exhibit topological order is the presence of long-range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a natural framework for the parameterization of gapped ground state wavefunctions which allows one to characterize topological order in terms of the virtual symmetries
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Slow Decay of Waves in Gravitational Solitons Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-06 Sharmila Gunasekaran, Hari K. Kunduri
We consider a family of globally stationary (horizonless), asymptotically flat solutions of five-dimensional supergravity. We prove that massless linear scalar waves in such soliton spacetimes cannot have a uniform decay rate faster than inverse logarithmically in time. This slow decay can be attributed to the stable trapping of null geodesics. Our proof uses the construction of quasimodes which are
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BV and BFV for the H-Twisted Poisson Sigma Model Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-06 Noriaki Ikeda, Thomas Strobl
We present the BFV and the BV extension of the Poisson sigma model (PSM) twisted by a closed 3-form H. There exist superfield versions of these functionals such as for the PSM and, more generally, for the AKSZ sigma models. However, in contrast to those theories, they depend on the Euler vector field of the source manifold and contain terms mixing data from the source and the target manifold. Using
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A New Symmetry of the Colored Alexander Polynomial Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-05 V. Mishnyakov, A. Sleptsov, N. Tselousov
We present a new conjectural symmetry of the colored Alexander polynomial, that is the specialization of the quantum \(\mathfrak {sl}_N\) invariant widely known as the colored HOMFLY-PT polynomial. We provide arguments in support of the existence of the symmetry by studying the loop expansion and the character expansion of the colored HOMFLY-PT polynomial. We study the constraints this symmetry imposes
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Exponential Decay of Correlations for Gibbs Measures and Semiflows over $$C^{1+\alpha }$$ C 1 + α Piecewise Expanding Maps Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-04 Diego Daltro, Paulo Varandas
We consider suspension (semi)flows over \({C}^{1+\alpha }\) full-branch Markov piecewise expanding interval maps and piecewise hyperbolic maps and prove exponential decay of correlations with respect to Gibbs measures associated with piecewise Hölder continuous potentials. As a consequence, typical codimension one attractors of \(C^{1+\alpha }\) Axiom A flows have exponential decay of correlations
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Exactness of Linear Response in the Quantum Hall Effect Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-04 Sven Bachmann, Wojciech De Roeck, Martin Fraas, Markus Lange
In general, linear response theory expresses the relation between a driving and a physical system’s response only to first order in perturbation theory. In the context of charge transport, this is the linear relation between current and electromotive force expressed in Ohm’s law. We show here that in the case of the quantum Hall effect, all higher-order corrections vanish. We prove this in a fully
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Invariant Measure for Stochastic Schrödinger Equations Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-02 T. Benoist, M. Fraas, Y. Pautrat, C. Pellegrini
Quantum trajectories are Markov processes that describe the time evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solutions of the so-called Stochastic Schrödinger Equations, which are nonlinear stochastic differential equations driven by Poisson and Wiener processes. This paper is devoted to the study of the invariant measures of quantum
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Chiral Floquet Systems and Quantum Walks at Half-Period Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-02 C. Cedzich, T. Geib, A. H. Werner, R. F. Werner
We classify chiral symmetric periodically driven quantum systems on a one-dimensional lattice. The driving process is local, can be continuous, or discrete in time, and we assume a gap condition for the corresponding Floquet operator. The analysis is in terms of the unitary operator at a half-period, the half-step operator. We give a complete classification of the connected classes of half-step operators
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Bisynchronous Games and Factorizable Maps Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-02 Vern I. Paulsen, Mizanur Rahaman
We introduce a new class of non-local games and corresponding densities, which we call bisynchronous. Bisynchronous games are a subclass of synchronous games and exhibit many interesting symmetries when the algebra of the game is considered. We develop a close connection between these non-local games and the theory of quantum groups which recently surfaced in studies of graph isomorphism games. When
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Future Stability of the FLRW Spacetime for a Large Class of Perfect Fluids Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-01 Chao Liu, Changhua Wei
We establish the future nonlinear stability of Friedmann–Lemaître–Robertson–Walker (FLRW) solutions to the Einstein–Euler equations of the universe filled with a large class of perfect fluids (the equations of state are allowed to be certain nonlinear or linear types both). Several previous results as specific examples can be covered in the results of this article. We emphasize that the future stability
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Asymptotic Gluing of Shear-Free Hyperboloidal Initial Data Sets Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-01 Paul T. Allen, James Isenberg, John M. Lee, Iva Stavrov Allen
We present a procedure for asymptotic gluing of hyperboloidal initial data sets for the Einstein field equations that preserves the shear-free condition. Our construction is modeled on the gluing construction in Isenberg et al. (Ann Henri Poincaré 11(5):881–927, 2010), but with significant modifications that incorporate the shear-free condition. We rely on the special Hölder spaces, and the corresponding
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Classifying Space for Quantum Contextuality Ann. Henri Poincaré (IF 1.489) Pub Date : 2021-01-01 Cihan Okay, Daniel Sheinbaum
We construct a topological space to study contextuality in quantum mechanics. The resulting space is a classifying space in the sense of algebraic topology. Cohomological invariants of our space correspond to physical quantities relevant to the study of contextuality. Within this framework the Wigner function of a quantum state can be interpreted as a class in the twisted K-theory of the classifying
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Bose–Einstein Condensation Beyond the Gross–Pitaevskii Regime Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-12-26 Arka Adhikari, Christian Brennecke, Benjamin Schlein
We consider N bosons in a box with volume one, interacting through a two-body potential with scattering length of the order \(N^{-1+\kappa }\), for \(\kappa >0\). Assuming that \(\kappa \in (0;1/43)\), we show that low-energy states exhibit Bose–Einstein condensation and we provide bounds on the expectation and on higher moments of the number of excitations.
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Dynamical C*-algebras and Kinetic Perturbations Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-12-23 Detlev Buchholz, Klaus Fredenhagen
The framework of dynamical C*-algebras for scalar fields in Minkowski space, based on local scattering operators, is extended to theories with locally perturbed kinetic terms. These terms encode information about the underlying spacetime metric, so the causality relations between the scattering operators have to be adjusted accordingly. It is shown that the extended algebra describes scalar quantum
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Weyl Law on Asymptotically Euclidean Manifolds Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-12-23 Sandro Coriasco, Moritz Doll
We study the asymptotic behaviour of the eigenvalue counting function for self-adjoint elliptic linear operators defined through classical weighted symbols of order (1, 1), on an asymptotically Euclidean manifold. We first prove a two-term Weyl formula, improving previously known remainder estimates. Subsequently, we show that under a geometric assumption on the Hamiltonian flow at infinity, there
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On the Correlation Between Nodal and Nonzero Level Sets for Random Spherical Harmonics Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-12-01 Domenico Marinucci, Maurizia Rossi
We study the correlation between the nodal length of random spherical harmonics and the length of a nonzero level set. We show that the correlation is asymptotically zero, while the partial correlation after removing the effect of the random \(L^2\)-norm of the eigenfunctions is asymptotically one.
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Algebraic Approach to Bose–Einstein Condensation in Relativistic Quantum Field Theory: Spontaneous Symmetry Breaking and the Goldstone Theorem Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-12-01 Romeo Brunetti, Klaus Fredenhagen, Nicola Pinamonti
We construct states describing Bose–Einstein condensates at finite temperature for a relativistic massive complex scalar field with \(|\varphi |^4\)-interaction. We start with the linearized theory over a classical condensate and construct interacting fields by perturbation theory. Using the concept of thermal masses, equilibrium states at finite temperature can be constructed by the methods developed
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The exponential decay of eigenfunctions for tight-binding Hamiltonians via landscape and dual landscape functions Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-27 Wei Wang, Shiwen Zhang
We consider the discrete Schrödinger operator \(H=-\Delta +V\) on a cube \(M\subset {{\mathbb {Z}}}^d\), with periodic or Dirichlet (simple) boundary conditions. We use a hidden landscape function u, defined as the solution of an inhomogeneous boundary problem with uniform right-hand side for H, to predict the location of the localized eigenfunctions of H. Explicit bounds on the exponential decay of
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On the Mathematical Foundations of Causal Fermion Systems in Minkowski Space Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-23 Marco Oppio
The emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski space. After a brief recap of the Dirac equation and its solution space, in order to allow for the effects of a possibly nonstandard structure of spacetime at the Planck scale, a regularization by a smooth cutoff in momentum space is introduced, and its properties
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Partially volume expanding diffeomorphisms Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-23 Shaobo Gan, Ming Li, Marcelo Viana, Jiagang Yang
We call a partially hyperbolic diffeomorphism partially volume expanding if the Jacobian restricted to any hyperplane that contains the unstable bundle \(E^u\) is larger than 1. This is a \(C^1\) open property. We show that any \(C^{1+}\) partially volume expanding diffeomorphisms admits finitely many physical measures, and the union of their basins has full volume.
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n -Laplacians on Metric Graphs and Almost Periodic Functions: I Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-22 Pavel Kurasov, Jacob Muller
The spectra of n-Laplacian operators \((-\Delta )^n\) on finite metric graphs are studied. An effective secular equation is derived and the spectral asymptotics are analysed, exploiting the fact that the secular function is close to a trigonometric polynomial. The notion of the quasispectrum is introduced, and its uniqueness is proved using the theory of almost periodic functions. To achieve this,
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Trigonometric Real Form of the Spin RS Model of Krichever and Zabrodin Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-21 M. Fairon, L. Fehér, I. Marshall
We investigate the trigonometric real form of the spin Ruijsenaars–Schneider system introduced, at the level of equations of motion, by Krichever and Zabrodin in 1995. This pioneering work and all earlier studies of the Hamiltonian interpretation of the system were performed in complex holomorphic settings; understanding the real forms is a non-trivial problem. We explain that the trigonometric real
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Sharp Asymptotics for the Solutions of the Three-Dimensional Massless Vlasov–Maxwell System with Small Data Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-20 Léo Bigorgne
This paper is concerned with the asymptotic properties of the small data solutions to the massless Vlasov–Maxwell system in 3d. We use vector field methods to derive almost optimal decay estimates in null directions for the electromagnetic field, the particle density and their derivatives. No compact support assumption in x or v is required on the initial data, and the decay in v is in particular initially
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A New Approach to Transport Coefficients in the Quantum Spin Hall Effect Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-18 Giovanna Marcelli, Gianluca Panati, Stefan Teufel
We investigate some foundational issues in the quantum theory of spin transport, in the general case when the unperturbed Hamiltonian operator \(H_0\) does not commute with the spin operator in view of Rashba interactions, as in the typical models for the quantum spin Hall effect. A gapped periodic one-particle Hamiltonian \(H_0\) is perturbed by adding a constant electric field of intensity \(\varepsilon
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Supercritical Poincaré–Andronov–Hopf Bifurcation in a Mean-Field Quantum Laser Equation Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-09 F. Fagnola, C. M. Mora
We deal with the dynamical system properties of a Gorini–Kossakowski–Sudarshan–Lindblad equation with mean-field Hamiltonian that models a simple laser by applying a mean-field approximation to a quantum system describing a single-mode optical cavity and a set of two-level atoms, each coupled to a reservoir. We prove that the mean-field quantum master equation has a unique regular stationary solution
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Global Evolution of the U(1) Higgs Boson: Nonlinear Stability and Uniform Energy Bounds Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-07 Shijie Dong, Philippe G. LeFloch, Zoe Wyatt
Relying on the hyperboloidal foliation method, we establish the nonlinear stability of the ground state of the U(1) standard model of electroweak interactions. This amounts to establishing a global-in-time theory for the initial value problem for a nonlinear wave–Klein–Gordon system that couples (Dirac, scalar, gauge) massive equations together. In particular, we investigate here the Dirac equation
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Non-compact Quantum Graphs with Summable Matrix Potentials Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-04 Yaroslav Granovskyi, Mark Malamud, Hagen Neidhardt
Let \(\mathcal {G}\) be a metric non-compact connected graph with finitely many edges. The main object of the paper is the Hamiltonian \(\mathbf{H}_{\alpha }\) associated in \(L^2(\mathcal {G};\mathbb {C}^m)\) with a matrix Sturm–Liouville expression and boundary delta-type conditions at each vertex. Assuming that the potential matrix is summable and applying the technique of boundary triplets and
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Spectral Properties of Schrödinger Operators Associated with Almost Minimal Substitution Systems Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-11-03 Benjamin Eichinger, Philipp Gohlke
We study the spectral properties of ergodic Schrödinger operators that are associated with a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go beyond minimality, unique ergodicity and linear complexity. In some parameter region, we are naturally in the setting of an infinite ergodic measure. The almost sure
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A Non-Hermitian Generalisation of the Marchenko–Pastur Distribution: From the Circular Law to Multi-criticality Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-29 Gernot Akemann, Sung-Soo Byun, Nam-Gyu Kang
We consider the complex eigenvalues of a Wishart type random matrix model \(X=X_1 X_2^*\), where two rectangular complex Ginibre matrices \(X_{1,2}\) of size \(N\times (N+\nu )\) are correlated through a non-Hermiticity parameter \(\tau \in [0,1]\). For general \(\nu =O(N)\) and \(\tau \), we obtain the global limiting density and its support, given by a shifted ellipse. It provides a non-Hermitian
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Condition Numbers for Real Eigenvalues in the Real Elliptic Gaussian Ensemble Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-27 Yan V. Fyodorov, Wojciech Tarnowski
We study the distribution of the eigenvalue condition numbers \(\kappa _i=\sqrt{ ({\mathbf{l}}_i^* {\mathbf{l}}_i)({\mathbf{r}}_i^* {\mathbf{r}}_i)}\) associated with real eigenvalues \(\lambda _i\) of partially asymmetric \(N\times N\) random matrices from the real Elliptic Gaussian ensemble. The large values of \(\kappa _i\) signal the non-orthogonality of the (bi-orthogonal) set of left \({\mathbf{l}}_i\)
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Racah Problems for the Oscillator Algebra, the Lie Algebra $$\mathfrak {sl}_n$$ sl n , and Multivariate Krawtchouk Polynomials Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-21 Nicolas Crampé, Wouter van de Vijver, Luc Vinet
The oscillator Racah algebra \(\mathcal {R}_n(\mathfrak {h})\) is realized by the intermediate Casimir operators arising in the multifold tensor product of the oscillator algebra \(\mathfrak {h}\). An embedding of the Lie algebra \(\mathfrak {sl}_{n-1}\) into \(\mathcal {R}_n(\mathfrak {h})\) is presented. It relates the representation theory of the two algebras. We establish the connection between
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Limiting Absorption Principle for Discrete Schrödinger Operators with a Wigner–von Neumann Potential and a Slowly Decaying Potential Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-20 Sylvain Golénia, Marc-Adrien Mandich
We consider discrete Schrödinger operators on \(\mathbb {Z}^d\) for which the perturbation consists of the sum of a long-range-type potential and a Wigner–von Neumann-type potential. Still working in a framework of weighted Mourre theory, we improve the limiting absorption principle (LAP) that was obtained in Mandich (J Funct Anal 272(6):2235–2272, 2017). To our knowledge, this is a new result even
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A Conformal Infinity Approach to Asymptotically $$\text {AdS}_2\times S^{n-1}$$ AdS 2 × S n - 1 Spacetimes Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-15 Gregory J. Galloway, Melanie Graf, Eric Ling
It is well known that the spacetime \(\text {AdS}_2\times S^2\) arises as the ‘near-horizon’ geometry of the extremal Reissner–Nordstrom solution, and for that reason, it has been studied in connection with the AdS/CFT correspondence. Motivated by a conjectural viewpoint of Juan Maldacena, Galloway and Graf (Adv Theor Math Phys 23(2):403–435, 2019) studied the rigidity of asymptotically \(\text {AdS}_2\times
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Averages of Products and Ratios of Characteristic Polynomials in Polynomial Ensembles Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-14 Gernot Akemann, Eugene Strahov, Tim R. Würfel
Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external field, that may serve as schematic models of quantum field theories with temperature. We first analyse expectation values of ratios of an equal number of characteristic
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Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-13 Krzysztof Myśliwy, Robert Seiringer
We consider the quantum mechanical many-body problem of a single impurity particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the Hamiltonian of this system in the mean-field limit and rigorously show that, at low energies, the problem is well described by the Fröhlich polaron model.
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Thermal Stability of the Nagaoka–Thouless Theorems Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-13 Tadahiro Miyao
We prove that the Aizenman–Lieb theorem on ferromagnetism in the Hubbard model holds true even if the electron–phonon interactions and the electron–photon interactions are taken into account. Our proof is based on path integral representations of the partition functions.
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General Toeplitz Matrices Subject to Gaussian Perturbations Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-13 Johannes Sjöstrand, Martin Vogel
We study the spectra of general \(N\times N\) Toeplitz matrices given by symbols in the Wiener Algebra perturbed by small complex Gaussian random matrices, in the regime \(N\gg 1\). We prove an asymptotic formula for the number of eigenvalues of the perturbed matrix in smooth domains. We show that these eigenvalues follow a Weyl law with probability sub-exponentially close to 1, as \(N\gg 1\), in particular
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Stability of the Enhanced Area Law of the Entanglement Entropy Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-10 Peter Müller, Ruth Schulte
We consider a multi-dimensional continuum Schrödinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper bound and a lower bound on the bipartite entanglement entropy of the ground state of the corresponding quasi-free Fermi gas. The bounds prove that the scaling behaviour of the entanglement entropy remains a logarithmically
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Hamiltonian Perturbations at the Second-Order Approximation Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-07 Di Yang
Integrability condition of Hamiltonian perturbations of integrable Hamiltonian PDEs of hydrodynamic type up to the second-order approximation is considered. Under a nondegeneracy assumption, we show that the Hamiltonian perturbation at the first-order approximation is integrable if and only if it is trivial, and that under a further assumption, the Hamiltonian perturbation at the second-order approximation
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Ruelle Zeta Function from Field Theory Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-06 Charles Hadfield, Santosh Kandel, Michele Schiavina
We propose a field-theoretic interpretation of Ruelle zeta function and show how it can be seen as the partition function for BF theory when an unusual gauge-fixing condition on contact manifolds is imposed. This suggests an alternative rephrasing of a conjecture due to Fried on the equivalence between Ruelle zeta function and analytic torsion, in terms of homotopies of Lagrangian submanifolds.
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A Supersymmetric Hierarchical Model for Weakly Disordered 3 d Semimetals Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-06 Giovanni Antinucci, Luca Fresta, Marcello Porta
In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point
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Limit Theorems for Random Expanding or Anosov Dynamical Systems and Vector-Valued Observables Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-10-01 Davor Dragičević, Yeor Hafouta
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic (Anosov) dynamics developed by the first author et al. to establish quenched versions of the large deviation principle, central limit theorem and the local central limit theorem for vector-valued observables. We stress that the previous works considered exclusively the
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On the Spectrum of the Local $${\mathbb {P}}^2$$ P 2 Mirror Curve Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-29 Rinat Kashaev, Sergey Sergeev
We address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi–Yau threefold called local \({\mathbb {P}}^2\) in the case of complex values of Planck’s constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations.
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The Mass of an Asymptotically Hyperbolic Manifold with a Non-compact Boundary Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-25 Sérgio Almaraz, Levi Lopes de Lima
We define a mass-type invariant for asymptotically hyperbolic manifolds with a non-compact boundary which are modelled at infinity on the hyperbolic half-space and prove a sharp positive mass inequality in the spin case under suitable dominant energy conditions. As an application, we show that any such manifold which is Einstein and either has a totally geodesic boundary or is conformally compact and
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Fisher Information and Logarithmic Sobolev Inequality for Matrix-Valued Functions Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-25 Li Gao, Marius Junge, Nicholas LaRacuente
We prove a version of Talagrand’s concentration inequality for subordinated sub-Laplacians on a compact Riemannian manifold using tools from noncommutative geometry. As an application, motivated by quantum information theory, we show that on a finite-dimensional matrix algebra the set of self-adjoint generators satisfying a tensor stable modified logarithmic Sobolev inequality is dense.
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Lieb–Robinson Bounds and Strongly Continuous Dynamics for a Class of Many-Body Fermion Systems in $${\mathbb {R}}^d$$ R d Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-24 Martin Gebert, Bruno Nachtergaele, Jake Reschke, Robert Sims
We introduce a class of UV-regularized two-body interactions for fermions in \({\mathbb {R}}^d\) and prove a Lieb–Robinson estimate for the dynamics of this class of many-body systems. As a step toward this result, we also prove a propagation bound of Lieb–Robinson type for Schrödinger operators. We apply the propagation bound to prove the existence of infinite-volume dynamics as a strongly continuous
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Low-Lying Eigenvalues and Convergence to the Equilibrium of Some Piecewise Deterministic Markov Processes Generators in the Small Temperature Regime Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-22 Arnaud Guillin, Boris Nectoux
In this work, we study the number of small eigenvalues and the convergence to the equilibrium of the Bouncy Particle Sampler process and the zigzag process generators in the small temperature regime. Such processes, which fall in the class of Piecewise Deterministic Markov Processes, are non-diffusive and non-reversible. They have recently been used a lot for simulation issues, falling in the domain
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Sharp Large Deviations for Hyperbolic Flows Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-22 Vesselin Petkov, Luchezar Stoyanov
For hyperbolic flows \(\varphi _t\), we examine the Gibbs measure of points w for which $$\begin{aligned} \int _0^T G(\varphi _t w) \hbox {d}t - a T \in (- e^{-\epsilon n}, e^{- \epsilon n}) \end{aligned}$$ as \(n \rightarrow \infty \) and \(T \ge n\), provided \(\epsilon > 0\) is sufficiently small. This is similar to local central limit theorems. The fact that the interval \((- e^{-\epsilon n}, e^{-
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Scale-free Unique Continuation Estimates and Logvinenko–Sereda Theorems on the Torus Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-22 Michela Egidi, Ivan Veselić
We study uncertainty principles for function classes on the torus. The classes are defined in terms of spectral subspaces of the energy or the momentum, respectively. In our main theorems, the support of the Fourier transform of the considered functions is allowed to be contained in (a finite number of) d-dimensional cubes. The estimates we obtain do not depend on the size of the torus and the position
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On Induction for Twisted Representations of Conformal Nets Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-11 Ryo Nojima
For a given finite index inclusion of strongly additive conformal nets \(\mathcal {B}\subset \mathcal {A}\) and a compact group \(G < {{\,\mathrm{Aut}\,}}(\mathcal {A}, \mathcal {B})\), we consider the induction and the restriction procedures for twisted representations. Let \(G' < {{\,\mathrm{Aut}\,}}(\mathcal {B})\) be the group obtained by restricting each element of G to \(\mathcal {B}\). We introduce
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Correction to: On Bianchi Type $$\hbox {VI}_0$$ VI 0 Spacetimes with Orthogonal Perfect Fluid Matter Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-09-07 Hans Oude Groeniger
Unfortunately, the corresponding author name was incorrectly published in the original version.
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A Local Energy Estimate for Wave Equations on Metrics Asymptotically Close to Kerr Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-08-27 Hans Lindblad, Mihai Tohaneanu
In this article, we prove a local energy estimate for the linear wave equation on metrics with slow decay to a Kerr metric with small angular momentum. As an application, we study the quasilinear wave equation \(\Box _{g(u, t, x)} u = 0\) where the metric g(u, t, x) is close (and asymptotically equal) to a Kerr metric with small angular momentum g(0, t, x). Under suitable assumptions on the metric
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Adiabatic Transitions in a Two-Level System Coupled to a Free Boson Reservoir Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-08-27 Alain Joye, Marco Merkli, Dominique Spehner
We consider a time-dependent two-level quantum system interacting with a free Boson reservoir. The coupling is energy conserving and depends slowly on time, as does the system Hamiltonian, with a common adiabatic parameter \(\varepsilon \). Assuming that the system and reservoir are initially decoupled, with the reservoir in equilibrium at temperature \(T\ge 0\), we compute the transition probability
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Conformal Contact Terms and Semi-local Terms Ann. Henri Poincaré (IF 1.489) Pub Date : 2020-08-19 Yu Nakayama
We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables, but they do appear in physically important correlation functions such as (anomalous) Ward–Takahashi identities or Schwinger–Dyson equations. We develop some tools such as embedding space delta functions and effective
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