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Mathematical Physics papers — page 191

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Perfect t-embeddings of uniformly weighted Aztec diamonds and tower graphs
In this work we study a sequence of perfect t-embeddings of uniformly weighted Aztec diamonds. We show that these perfect t-embeddings can be used to prove convergence of gradients of height…
Tomas Berggren, Matthew Nicoletti, Marianna RusskikhMar 17, 2023
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J\'anossy densities and Darboux transformations for the Stark and cylindrical KdV equations
We study J\'anossy densities of a randomly thinned Airy kernel determinantal point process. We prove that they can be expressed in terms of solutions to the Stark and cylindrical Korteweg-de Vries…
Tom Claeys, Gabriel Glesner, Giulio Ruzza et al.Mar 17, 2023
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Footprint of a topological phase transition on the density of states
For a generalized Su-Schrieffer-Heeger model the energy zero is always critical and hyperbolic in the sense that all reduced transfer matrices commute and have their spectrum off the unit circle.…
Joris De Moor, Christian Sadel, Hermann Schulz-BaldesMar 17, 2023
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Spectral localizer for line-gapped non-hermitian systems
Short-ranged and line-gapped non-hermitian Hamiltonians have strong topological invariants given by an index of an associated Fredholm operator. It is shown how these invariants can be accessed via…
Alexander Cerjan, Lars Koekenbier, Hermann Schulz-BaldesMar 16, 2023
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Properties of 2D anyon gas
An overview is given of the 2D many-anyon gas, including its definition (both for ideal and certain less-than-ideal particles, as well as for abelian and nonabelian braid group representations), its…
Douglas LundholmMar 16, 2023
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Topological edge states of 1D chains and index theory
We provide an elementary proof and refinement of a well-known idea from physics: a chiral-symmetric local Hamiltonian on a half-space has the same signed number of edge-localized states with energies…
Guo Chuan ThiangMar 16, 2023
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Quaternion Algebra Approach to Nonlinear Schr\"odinger Equations with Nonvanishing Boundary Conditions
In this article we apply quaternionic linear algebra and quaternionic linear system theory to develop the inverse scattering transform theory for the nonlinear Schr\"odinger equation with…
Francesco Demontis, Cornelis van der MeeMar 16, 2023
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On a new proof of the Okuyama--Sakai conjecture
In [41] Okuyama and Sakai gave a conjectural equality for the higher genus generalized Br\'ezin--Gross--Witten (BGW) free energies. In a recent work [46] we established the Hodge-BGW correspondence…
Di Yang, Qingsheng ZhangMar 16, 2023
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Symmetries and first integrals for variational ODEs with delay
A Lagrangian formalism for variational second-order delay ordinary differential equations (DODEs) is developed. The Noether operator identity for a DODE is established, which relates the invariance…
V. A. Dorodnitsyn, R. V. Kozlov, S. V. MeleshkoMar 16, 2023
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Law of large numbers and central limit theorem for ergodic quantum processes
A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are…
Lubashan Pathirana, Jeffrey SchenkerMar 15, 2023
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A Z2 invariant for chiral and particle-hole symmetric topological chains
We define a Z2-valued topological and gauge invariant associated to any 1-dimensional, translation-invariant topological insulator which satisfies either particle-hole symmetry or chiral…
Domenico Monaco, Gabriele PelusoMar 15, 2023
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Gaudin model for the multinomial distribution
The goal of the paper is to analyze a Gaudin model for a polynomial representation of the Kohno-Drinfeld Lie algebra associated with the multinomial distribution. The main result is the construction…
Plamen IlievMar 14, 2023
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Structural stability of the RG flow in the Gross-Neveu model
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 d=2 dimensional Euclidean space with a…
J. Dimock, Cheng YuanMar 14, 2023
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Asymptotics of non-integer moments of the logarithmic derivative of characteristic polynomials over SO(2N+1)
This work computes the asymptotics of the non-integer moments of the logarithmic derivative of characteristic polynomials of matrices from the SO(2N+1) ensemble. It follows from work of Alvarez and…
Emilia Alvarez, Pierre Bousseyroux, Nina C. SnaithMar 14, 2023
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Homotopical Foundations of Parametrized Quantum Spin Systems
In this paper, we present a homotopical framework for studying invertible gapped phases of matter from the point of view of infinite spin lattice systems, using the framework of algebraic quantum…
Agnes Beaudry, Michael Hermele, Juan Moreno et al.Mar 13, 2023
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Dynamical abelian anyons with bound states and scattering states
We introduce a family of quantum spin Hamiltonians on Z2 that can be regarded as perturbations of Kitaev's abelian quantum double models that preserve the gauge and duality symmetries of…
Sven Bachmann, Bruno Nachtergaele, Siddharth VadnerkarMar 13, 2023
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Existence proof of librational invariant tori in an averaged model of HD60532 planetary system
We investigate the long-term dynamics of HD60532, an extrasolar system hosting two giant planets orbiting in a 3:1 mean motion resonance. We consider an average approximation at order one in the…
Veronica Danesi, Ugo Locatelli, Marco SansotteraMar 12, 2023
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Information propagation in long-range quantum many-body systems
We study general lattice bosons with long-range hopping and long-range interactions decaying as |x-y|-α with α∈ (d+2,2d+1). We find a linear light cone for the information…
Marius Lemm, Carla Rubiliani, Israel Michael Sigal et al.Mar 11, 2023
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Hypergeometric identities related to Ruijsenaars systems
We present and prove hypergeometric identities which play a crucial role in the theory of Baxter operators in the Ruijsenaars model.
N. Belousov, S. Derkachov, S. Kharchev et al.Mar 11, 2023
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Baxter operators in Ruijsenaars hyperbolic system I. Commutativity of Q-operators
We introduce Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. We prove that they represent a commuting family of integral operators and also commute with Macdonald difference…
N. Belousov, S. Derkachov, S. Kharchev et al.Mar 11, 2023
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Baxter operators in Ruijsenaars hyperbolic system II. Bispectral wave functions
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…
N. Belousov, S. Derkachov, S. Kharchev et al.Mar 11, 2023
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Dynamics of the infinite discrete nonlinear Schr\"odinger equation
The discrete nonlinear Schr\"odinger equation on \(d\), \(d ≥ 1\) is an example of a dispersive nonlinear wave system. Being a Hamiltonian system that conserves also the \(2(d)\)-norm,…
Aleksis VuoksenmaaMar 11, 2023
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Weighted CLR type bounds in two dimensions
We derive weighted versions of the Cwikel-Lieb-Rozenblum inequality for the Schr\"odinger operator in two dimensions with a nontrivial Aharonov-Bohm magnetic field. Our bounds capture the optimal…
Rupert L. Frank, Ari Laptev, Larry ReadMar 10, 2023
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Intrinsic nonlinear elasticity: An exterior calculus formulation
In this paper we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such…
Ramy Rashad, Andrea Brugnoli, Federico Califano et al.Mar 10, 2023
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Stability of charge density waves in electron-phonon systems
We demonstrate that electron-phonon interactions enhance the stability of charge density waves in low-temperature phases of many-electron systems. Our proof method involves an appropriate application…
Tadahiro MiyaoMar 10, 2023
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