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Structural Stability of the RG Flow in the Gross–Neveu Model Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-03-18 J. Dimock, Cheng Yuan
We study flow of renormalization group (RG) transformations for the massless Gross–Neveu model in a non-perturbative formulation. The model is defined on a two-dimensional Euclidean space with a finite volume. The quadratic approximation to the flow stays bounded after suitable renormalization. We show that for weak coupling this property also is true for the complete flow. As an application we prove
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An Index for Quantum Cellular Automata on Fusion Spin Chains Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-03-11 Corey Jones, Junhwi Lim
Interpreting the GNVW index for 1D quantum cellular automata (QCA) in terms of the Jones index for subfactors leads to a generalization of the index defined for QCA on more general abstract spin chains. These include fusion spin chains, which arise as the local operators invariant under a global (categorical/MPO) symmetry, and as the boundary operators of 2D topological codes. We show that for the
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Synchronous Values of Games Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-03-04 J. William Helton, Hamoon Mousavi, Seyed Sajjad Nezhadi, Vern I. Paulsen, Travis B. Russell
We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy. However, we give examples of synchronous games, in particular graph colouring games, with synchronous value that is strictly smaller than their ordinary value. Thus, the optimal strategy for a synchronous game need not be
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Nodal Set Openings on Perturbed Rectangular Domains Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-03-02 Thomas Beck, Marichi Gupta, Jeremy Marzuola
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On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang–Mills Equation Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-03-01
Abstract We introduce the idea of constructing recursion operators for full-fledged nonlocal symmetries and apply it to the reduced quasi-classical self-dual Yang–Mills equation. It turns out that the discovered recursion operators can be interpreted as infinite-dimensional matrices of differential functions which act on the generating vector functions of the nonlocal symmetries simply by matrix multiplication
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Dimensional reduction for a system of 2D anyons Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-29
Abstract Anyons with a statistical phase parameter \(\alpha \in (0,2)\) are a kind of quasi-particles that, for topological reasons, only exist in a 1D or 2D world. We consider the dimensional reduction for a 2D system of anyons in a tight wave guide. More specifically, we study the 2D magnetic gauge picture model with an imposed anisotropic harmonic potential that traps particles much stronger in
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Universality of Graph Homomorphism Games and the Quantum Coloring Problem Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-28 Samuel J. Harris
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Deformation and Quantisation Condition of the $$\mathcal {Q}$$ -Top Recursion Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-21 Kento Osuga
We consider a deformation of a family of hyperelliptic refined spectral curves and investigate how deformation effects appear in the hyperelliptic refined topological recursion as well as the \(\mathcal {Q}\)-top recursion. We then show a coincidence between a deformation condition and a quantisation condition in terms of the \(\mathcal {Q}\)-top recursion on a degenerate elliptic curve. We also discuss
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Negative Curvature Constricts the Fundamental Gap of Convex Domains Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-21 Gabriel Khan, Xuan Hien Nguyen
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Higher Deformation Quantization for Kapustin–Witten Theories Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-16 Chris Elliott, Owen Gwilliam, Brian R. Williams
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Analytic States in Quantum Field Theory on Curved Spacetimes Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-16
Abstract We discuss high energy properties of states for (possibly interacting) quantum fields in curved spacetimes. In particular, if the spacetime is real analytic, we show that an analogue of the timelike tube theorem and the Reeh–Schlieder property hold with respect to states satisfying a weak form of microlocal analyticity condition. The former means the von Neumann algebra of observables of a
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Convergence of Dynamics on Inductive Systems of Banach Spaces Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-14 Lauritz van Luijk, Alexander Stottmeister, Reinhard F. Werner
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Cosmological Einstein- $$\lambda $$ -Perfect-Fluid Solutions with Asymptotic Dust or Asymptotic Radiation Equations of State Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-09 Helmut Friedrich
This article introduces the notions of asymptotic dust and asymptotic radiation equations of state. With these non-linear generalizations of the well known dust or (incoherent) radiation equations of state the perfect-fluid equations lose any conformal covariance or privilege. We analyse the conformal field equations induced with these equations of state. It is shown that the Einstein-\(\lambda \)-perfect-fluid
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A Classification of Supersymmetric Kaluza–Klein Black Holes with a Single Axial Symmetry Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-08 David Katona
We extend the recent classification of five-dimensional, supersymmetric asymptotically flat black holes with only a single axial symmetry to black holes with Kaluza–Klein asymptotics. This includes a similar class of solutions for which the supersymmetric Killing field is generically timelike, and the corresponding base (orbit space of the supersymmetric Killing field) is of multi-centred Gibbons–Hawking
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Limit Theorems for the Cubic Mean-Field Ising Model Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-08
Abstract We study a mean-field spin model with three- and two-body interactions. The equilibrium measure for large volumes is shown to have three pure states, the phases of the model. They include the two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. We prove that the central limit theorem holds for a suitably rescaled magnetization, while
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Supergroups, q-Series and 3-Manifolds Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-05 Francesca Ferrari, Pavel Putrov
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On Unitarity of the Scattering Operator in Non-Hermitian Quantum Mechanics Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-05
Abstract We consider the Schrödinger operator with regular short range complex-valued potential in dimension \(d\ge 1\) . We show that, for \(d\ge 2\) , the unitarity of scattering operator for this Hamiltonian at high energies implies the reality of the potential (that is Hermiticity of Hamiltonian). In contrast, for \(d=1\) , we present complex-valued exponentially localized soliton potentials with
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A KAM Approach to the Inviscid Limit for the 2D Navier–Stokes Equations Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-05 Luca Franzoi, Riccardo Montalto
In this paper, we investigate the inviscid limit \(\nu \rightarrow 0\) for time-quasi-periodic solutions of the incompressible Navier–Stokes equations on the two-dimensional torus \({\mathbb {T}}^2\), with a small time-quasi-periodic external force. More precisely, we construct solutions of the forced Navier–Stokes equation, bifurcating from a given time quasi-periodic solution of the incompressible
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Perturbative BF Theory in Axial, Anosov Gauge Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-02-03 Michele Schiavina, Thomas Stucker
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Quantum Energy Inequalities in Integrable Models with Several Particle Species and Bound States Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-30 Henning Bostelmann, Daniela Cadamuro, Jan Mandrysch
We investigate lower bounds to the time-smeared energy density, so-called quantum energy inequalities (QEI), in the class of integrable models of quantum field theory. Our main results are a state-independent QEI for models with constant scattering function and a QEI at one-particle level for generic models. In the latter case, we classify the possible form of the stress-energy tensor from first principles
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Ground States for Infrared Renormalized Translation-Invariant Non-Relativistic QED Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-29 David Hasler, Oliver Siebert
We consider a translation-invariant Pauli–Fierz model describing a non-relativistic charged quantum mechanical particle interacting with the quantized electromagnetic field. The charged particle may be spinless or have spin one half. We decompose the Hamiltonian with respect to the total momentum into a direct integral of so-called fiber Hamiltonians. We perform an infrared renormalization, in the
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Resurgent Asymptotics of Jackiw–Teitelboim Gravity and the Nonperturbative Topological Recursion Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-29 Bertrand Eynard, Elba Garcia-Failde, Paolo Gregori, Danilo Lewański, Ricardo Schiappa
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Shuffling Algorithm for Coupled Tilings of the Aztec Diamond Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-27 David Keating, Matthew Nicoletti
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Baxter Operators in Ruijsenaars Hyperbolic System III: Orthogonality and Completeness of Wave Functions Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-22 N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin
In the previous paper, we showed that the wave functions of the quantum Ruijsenaars hyperbolic system diagonalize Baxter Q-operators. Using this property and duality relation, we prove orthogonality and completeness relations for the wave functions or, equivalently, unitarity of the corresponding integral transform.
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On the Convergence to the Non-equilibrium Steady State of a Langevin Dynamics with Widely Separated Time Scales and Different Temperatures Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-18 Diego Alberici, Nicolas Macris, Emanuele Mingione
We study the solution of the two-temperature Fokker–Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of convergence are estimated assuming the validity of logarithmic Sobolev inequalities for the conditional and marginal distributions of the limit measure. We show that
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Global Existence and Long-Time Behavior in the 1 + 1-Dimensional Principal Chiral Model with Applications to Solitons Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-16 Jessica Trespalacios
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Frobenius Algebras Associated with the $$\alpha $$ -Induction for Equivariantly Braided Tensor Categories Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-16 Mizuki Oikawa
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Circuit Equation of Grover Walk Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-10 Yusuke Higuchi, Etsuo Segawa
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The Singularities of Selberg- and Dotsenko–Fateev-Like Integrals Ann. Henri Poincaré (IF 1.5) Pub Date : 2024-01-03
Abstract We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ’s minimal models of 2D CFT as described by Felder & Silvotti and Dotsenko & Fateev (the “Coulomb gas formalism”). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is
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Robustness of Flat Bands on the Perturbed Kagome and the Perturbed Super-Kagome Lattice Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-28 Joachim Kerner, Matthias Täufer, Jens Wintermayr
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Stability of the Spectral Gap and Ground State Indistinguishability for a Decorated AKLT Model Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-27 Angelo Lucia, Alvin Moon, Amanda Young
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Local Hölder Stability in the Inverse Steklov and Calderón Problems for Radial Schrödinger Operators and Quantified Resonances Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-27 Thierry Daudé, Niky Kamran, François Nicoleau
We obtain Hölder stability estimates for the inverse Steklov and Calderón problems for Schrödinger operators corresponding to a special class of \(L^2\) radial potentials on the unit ball. These results provide an improvement on earlier logarithmic stability estimates obtained in Daudé et al. (J Geom Anal 31(2):1821–1854, 2021) in the case of the Schrödinger operators related to deformations of the
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$$L^2$$ -Decay Rate for Special Solutions to Critical Dissipative Nonlinear Schrödinger Equations Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-26 Takuya Sato
We consider the Cauchy problem of one-dimensional dissipative nonlinear Schrödinger equations with a critical power nonlinearity. In the previous work, Ogawa–Sato (Nonlinear Differ Equ Appl 27:18, 2020) showed the upper \(L^2\)-decay estimate of dissipative solutions in the analytic class. In this paper, we show that \(L^2\)-decay rate obtained in the previous work is optimal for special solutions
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Rademacher Expansion of a Siegel Modular Form for $${{\mathcal {N}}}= 4$$ Counting Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-25 Gabriel Lopes Cardoso, Suresh Nampuri, Martí Rosselló
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The Rotation Number for Almost Periodic Potentials with Jump Discontinuities and $$\delta $$ -Interactions Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-22 David Damanik, Meirong Zhang, Zhe Zhou
We consider one-dimensional Schrödinger operators with generalized almost periodic potentials with jump discontinuities and \(\delta \)-interactions. For operators of this kind, we introduce a rotation number in the spirit of Johnson and Moser. To do this, we introduce the concept of almost periodicity at a rather general level, and then the almost periodic function with jump discontinuities and \(\delta
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Differences Between Robin and Neumann Eigenvalues on Metric Graphs Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-19 Ram Band, Holger Schanz, Gilad Sofer
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Recurrence Relations and General Solution of the Exceptional Hermite Equation Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-12 Alfred Michel Grundland, Danilo Latini, Ian Marquette
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Expansion and Collapse of Spherically Symmetric Isotropic Elastic Bodies Surrounded by Vacuum Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-09 Thomas C. Sideris
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On the Fourier Analysis of the Einstein–Klein–Gordon System: Growth and Decay of the Fourier Constants Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-09 Athanasios Chatzikaleas
We consider the \((1+3)\)-dimensional Einstein equations with negative cosmological constant coupled to a spherically symmetric, massless scalar field and study perturbations around the anti-de Sitter spacetime. We derive the resonant systems, pick out vanishing secular terms and discuss issues related to small divisors. Most importantly, we rigorously establish (sharp, in most of the cases) asymptotic
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The Characteristic Gluing Problem for the Einstein Vacuum Equations: Linear and Nonlinear Analysis Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-12-07 Stefanos Aretakis, Stefan Czimek, Igor Rodnianski
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Particle Trajectories for Quantum Maps Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-11-27 Yonah Borns-Weil, Izak Oltman
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Non-trivial Bundles and Algebraic Classical Field Theory Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-11-22 Romeo Brunetti, Andrea Moro
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Baxter operators in Ruijsenaars hyperbolic system II: bispectral wave functions Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-11-20 N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin
In the previous paper, we introduced a commuting family of Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. In the present work, we show that the wave functions of the quantum system found by M. Hallnäs and S. Ruijsenaars also diagonalize Baxter operators. Using this property, we prove the conjectured duality relation for the wave function. As a corollary, we show that the wave function
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Entanglement Entropy of Ground States of the Three-Dimensional Ideal Fermi Gas in a Magnetic Field Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-11-07 Paul Pfeiffer, Wolfgang Spitzer
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Reconstruction of Vertex Algebras in Even Higher Dimensions Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-11-02 Bojko N. Bakalov, Nikolay M. Nikolov
Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to dimension one. In the case when D is even, we find natural conditions under which the converse passage is possible. These conditions include a unitary action of the
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Multiple Skew-Orthogonal Polynomials and 2-Component Pfaff Lattice Hierarchy Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-30 Shi-Hao Li, Bo-Jian Shen, Jie Xiang, Guo-Fu Yu
In this paper, we introduce multiple skew-orthogonal polynomials and investigate their connections with classical integrable systems. By using Pfaffian techniques, we show that multiple skew-orthogonal polynomials can be expressed by multi-component Pfaffian tau-functions upon appropriate deformations. Moreover, a two-component Pfaff lattice hierarchy, which is equivalent to the Pfaff–Toda hierarchy
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Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-24 Benjamin Delarue, Philipp Schütte, Tobias Weich
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Bulk Behaviour of Ground States for Relativistic Schrödinger Operators with Compactly Supported Potentials Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-20 Giacomo Ascione, József Lőrinczi
We propose a probabilistic representation of the ground states of massive and massless Schrödinger operators with a potential well in which the behaviour inside the well is described in terms of the moment-generating function of the first exit time from the well and the outside behaviour in terms of the Laplace transform of the first entrance time into the well. This allows an analysis of their behaviour
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An Operator-Algebraic Formulation of Self-testing Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-18 Connor Paddock, William Slofstra, Yuming Zhao, Yangchen Zhou
We give a new definition of self-testing for correlations in terms of states on \(C^*\)-algebras. We show that this definition is equivalent to the standard definition for any class of finite-dimensional quantum models which is closed, provided that the correlation is extremal and has a full-rank model in the class. This last condition automatically holds for the class of POVM quantum models, but does
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Airy Ideals, Transvections, and $${\mathcal {W}}(\mathfrak {sp}_{2N})$$ -Algebras Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-17 Vincent Bouchard, Thomas Creutzig, Aniket Joshi
In the first part of the paper, we propose a different viewpoint on the theory of higher Airy structures (or Airy ideals), which may shed light on its origin. We define Airy ideals in the \(\hbar \)-adic completion of the Rees Weyl algebra and show that Airy ideals are defined exactly such that they are always related to the canonical left ideal generated by derivatives by automorphisms of the Rees
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Hodge-Elliptic Genera, K3 Surfaces and Enumerative Geometry Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-11 Michele Cirafici
K3 surfaces play a prominent role in string theory and algebraic geometry. The properties of their enumerative invariants have important consequences in black hole physics and in number theory. To a K3 surface, string theory associates an Elliptic genus, a certain partition function directly related to the theory of Jacobi modular forms. A multiplicative lift of the Elliptic genus produces another
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Spectral and Combinatorial Aspects of Cayley-Crystals Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-05 Fabian R. Lux, Emil Prodan
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On the Well-Posedness and Stability of Cubic and Quintic Nonlinear Schrödinger Systems on $$\mathbb {T}^3$$ Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-03 Thomas Chen, Amie Bowles Urban
In this paper, we study cubic and quintic nonlinear Schrödinger systems on three-dimensional tori, with initial data in an adapted Hilbert space \(H^s_{{\underline{\lambda }}},\) and all of our results hold on rational and irrational rectangular, flat tori. In the cubic and quintic case, we prove local well-posedness for both focusing and defocusing systems. We show that local solutions of the defocusing
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Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-04 Benjamin Hinrichs, Oliver Matte
We consider the renormalized relativistic Nelson model in two spatial dimensions for a finite number of spinless, relativistic quantum mechanical matter particles in interaction with a massive scalar quantized radiation field. We find a Feynman–Kac formula for the corresponding semigroup and discuss some implications such as ergodicity and weighted \(L^p\) to \(L^q\) bounds, for external potentials
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Degenerate Perturbation Theory for Models of Quantum Field Theory with Symmetries Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-03 David Hasler, Markus Lange
We consider Hamiltonians of models describing non-relativistic quantum mechanical matter coupled to a relativistic field of bosons. If the free Hamiltonian has an eigenvalue, we show that this eigenvalue persists also for nonzero coupling. The eigenvalue of the free Hamiltonian may be degenerate provided there exists a symmetry group acting irreducibly on the eigenspace. Furthermore, if the Hamiltonian
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Decay Estimates for the Massless Vlasov Equation on Schwarzschild Spacetimes Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-03 Léo Bigorgne
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Pitchfork Bifurcation at Line Solitons for Nonlinear Schrödinger Equations on the Product Space $${\mathbb {R}}\times {\mathbb {T}}$$ Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-09-29 Takafumi Akahori, Yakine Bahri, Slim Ibrahim, Hiroaki Kikuchi
In this paper, we study the bifurcation problem from a line soliton for a stationary nonlinear Schrödinger equation on the product space \({\mathbb {R}}\times {\mathbb {T}}\). We extend earlier results to a larger class of the nonlinearity in the equation. The salient point of our analysis relies on a lower bound of solution to the “auxiliary equation” and then on the application of the Crandall–Rabinowitz
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Multiplicity and Concentration of Solutions for a Fractional Magnetic Kirchhoff Equation with Competing Potentials Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-10-01 Shengbing Deng, Wenshan Luo
This paper is concerned with the following fractional electromagnetic Kirchhoff equation with competing potentials and critical nonlinearity $$\begin{aligned} \left( a\varepsilon ^{2s}+b\varepsilon ^{4s-3} [u]_{A/\varepsilon }^{2}\right) (-\Delta )_{A/\varepsilon }^{s}u+V(x)u=f(|u|^{2})u+K(x)|u|^{2^{*}_{s}-2}u \quad \text{ in }\; {\mathbb {R}}^{3}, \end{aligned}$$ where \( \varepsilon >0 \) is a small
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Background Independence and the Adler–Bardeen Theorem Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-09-21 Jochen Zahn
We prove that for renormalizable Yang–Mills gauge theory with arbitrary compact gauge group (of at most a single abelian factor) and matter coupling, the absence of gauge anomalies can be established at the one-loop level. This proceeds by relating the gauge anomaly to perturbative agreement, which formalizes background independence.
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The Vanishing of Excess Heat for Nonequilibrium Processes Reaching Zero Ambient Temperature Ann. Henri Poincaré (IF 1.5) Pub Date : 2023-09-20 Faezeh Khodabandehlou, Christian Maes, Irene Maes, Karel Netočný