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Mathematical Physics papers — page 192

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Szego Kernel and Symplectic Aspects of Spectral Transform for Extended Spaces of Rational Matrices
We revisit the symplectic aspects of the spectral transform for matrix-valued rational functions with simple poles. We construct eigenvectors of such matrices in terms of the Szego kernel on the…
Marco Bertola, Dmitry Korotkin, Ramtin SasaniMar 9, 2023
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Phase transitions, KMS-condition and Decision Making
We consider a simple model of interacting agents asked to choose between "yes" and "not" to some given question. The agents are described in terms of spin variables, and they interact according to a…
Fabio BagarelloMar 9, 2023
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Schr\"odinger evolution in a low-density random potential: annealed convergence to the linear Boltzmann equation for general semiclassical Wigner measures
We consider solutions of the time-dependent Schr\"odinger equation for a potential localised at the points of a Poisson process. We prove convergence of the phase-space distribution in the annealed…
Søren MikkelsenMar 9, 2023
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Ergodic Archimedean dimers
We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be…
Henrik Schou Røising, Zhao ZhangMar 8, 2023
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Embedded trace operator for infinite metric trees
We consider a class of infinite weighted metric trees obtained as perturbations of self-similar regular trees. Possible definitions of the boundary traces of functions in the Sobolev space on such a…
Valentina Franceschi, Kiyan Naderi, Konstantin PankrashkinMar 8, 2023
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A simple approach to Lieb--Thirring type inequalities
In Nam Nam proved a Lieb--Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a…
Robert Seiringer, Jan Philip SolovejMar 8, 2023
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Subfactors and Mathematical Physics
This paper surveys the long-standing connections and impact between Vaughan Jones's theory of subfactors and various topics in mathematical physics, namely statistical mechanics,quantum field…
David E. Evans, Yasuyuki KawahigashiMar 8, 2023
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Duality and Macdonald difference operators
This note summarizes certain properties common to Macdonald, Koornwinder and Arthamonov-Shakirov q-difference operators, relating to the duality or bi-spectrality properties of their…
Philippe Di Francesco, Rinat KedemMar 7, 2023
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D-divisible quantum evolution families
We propose and explore a notion of decomposably divisible (D-divisible) differentiable quantum evolution families on matrix algebras. This is achieved by replacing the complete positivity…
Krzysztof SzczygielskiMar 7, 2023
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Quasi-free states on a class of algebras of multicomponent commutation relations
Multicomponent commutations relations (MCR) describe plektons, i.e., multicomponent quantum systems with a generalized statistics. In such systems, exchange of quasiparticles is governed by a unitary…
Eugene Lytvynov, Nedal OthmanMar 7, 2023
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Null Hamiltonian Yang-Mills theory: Soft symmetries and memory as superselection
Soft symmetries for Yang-Mills theory are shown to correspond to the residual Hamiltonian action of the gauge group on the Ashtekar-Streubel phase space, which is the result of a partial symplectic…
Aldo Riello, Michele SchiavinaMar 6, 2023
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Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree
We consider the Ising model with competing interactions and a nonzero external field on the Cayley tree of order two. We describe ground states and verify the Peierls condition for the model. Using a…
M. M. Rahmatullaev, M. A. Rasulova, J. N AsqarovMar 6, 2023
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Modified Green-Hyperbolic Operators
Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important…
Christopher J. FewsterMar 6, 2023
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Nonholonomic brackets: Eden revisited
The nonholonomic dynamics can be described by the so-called nonholonomic bracket in the constrained submanifold, which is a non-integrable modification of the Poisson bracket of the ambient space, in…
Manuel de León, Manuel Lainz, Asier López-Gordón et al.Mar 6, 2023
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Universal Constants, Law of Inertia and Emergent Geometry
In this paper, we only treat the law of inertia as the first principle, then a nontrivial geometry emerges by introducing more universal constants, in which the main ideas appearing in deformed…
Zhi Hu, Mulin Yan, Runhong ZongMar 5, 2023
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Recovering the shape of a quantum tree by scattering data
We consider a scattering problem generated by the Sturm-Liouville equation on a tree which consists of a equilateral compact subtree with a lead (a half-infinite edge) attached to this compact…
Vyacheslav PivovarchikMar 4, 2023
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Higher rank generalization of 11-vertex rational R-matrix: IRF-Vertex relations and associative Yang-Baxter equation
We study GLN rational R-matrix, which turns into the 11-vertex R-matrix in the N=2 case. First, we describe its relations to dynamical and semi-dynamical R-matrices using the…
K. Atalikov, A. ZotovMar 4, 2023
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A "lifting" method for exponential large deviation estimates and an application to certain non-stationary 1D lattice Anderson models
Proofs of localization for random Schr\"odinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman-Molchanov,…
Omar HurtadoMar 4, 2023
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Lagrangian trajectories and closure models in mixed quantum-classical dynamics
Mixed quantum-classical models have been proposed in several contexts to overcome the computational challenges of fully quantum approaches. However, current models typically suffer from long-standing…
Cesare Tronci, François Gay-BalmazMar 3, 2023
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Group theoretical derivation of consistent particle theories
Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The…
Giuseppe NisticòMar 3, 2023
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A Lorentzian renormalisation group equation for gauge theories
In a recent paper, with Drago and Pinamonti we have introduced a Wetterich-type flow equation for scalar fields on Lorentzian manifolds, using the algebraic approach to perturbative QFT. The equation…
Edoardo D'Angelo, Kasia RejznerMar 2, 2023
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Asymptotic step-like solutions to the singularly perturbed Burgers' equation
The paper deals with a problem of asymptotic step-like solutions to the Burgers' equation with variable coefficients and a small parameter. By means of the non-linear WKB method, the algorithm of…
Valerii Samoilenko, Yuliia Samoilenko, Elvira ZappaleMar 2, 2023
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Localization and Regularity of the Integrated Density of States for Schr\"odinger Operators on Zd with C2-cosine Like Quasi-periodic Potential
In this paper, we study the multidimensional lattice Schr\"odinger operators with C2-cosine like quasi-periodic (QP) potential. We establish quantitative Green's function estimates, the arithmetic…
Hongyi Cao, Yunfeng Shi, Zhifei ZhangMar 2, 2023
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A Pair of Non-Isometric Potentials With the Same Semiclassical Invariants
We show that there exist pairs of non-isometric potentials for the 1D semiclassical Schr\"odinger operator whose spectra agree up to O(h∞), yet their corresponding eigenvalues differ no less…
Matthew WestMar 2, 2023
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Polynomial algebras from Lie algebra reduction chains g ⊃ g'
We reexamine different examples of reduction chains g ⊃ g' of Lie algebras in order to show how the polynomials determining the commutant with respect to the subalgebra…
Rutwig Campoamor-Stursberg, Danilo Latini, Ian Marquette et al.Mar 2, 2023
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