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Mathematical Physics papers — page 196

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Chow's theorem for Hilbert Grassmannians as a Wigner-type theorem
Let H be an infinite-dimensional complex Hilbert space. Denote by G∞(H) the Grassmannian formed by closed subspaces of H whose dimension and codimension both are infinite. We…
Mark Pankov, Adam TycFeb 2, 2023
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The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems
A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems we provide a full…
Chokri Manai, Simone WarzelFeb 1, 2023
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Elastic solids with strain-gradient elastic boundary surfaces
Recent works have shown that in contrast to classical linear elastic fracture mechanics, endowing crack fronts in a brittle Green-elastic solid with Steigmann-Ogden surface elasticity yields a model…
Casey RodriguezJan 31, 2023
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An explicit form of the fundamental solution of the master equation for a jump-diffusion Ornstein-Uhlenbeck process
An integro-differential equation for the probability density of the generalized stochastic Ornstein-Uhlenbeck process with jump diffusion is considered. It is shown that for a certain ratio between…
Olga S. Rozanova, Nikolai A. KrutovJan 31, 2023
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Closed Form Expressions for Certain Improper Integrals of Mathematical Physics
We present new closed-form expressions for certain improper integrals of Mathematical Physics such as certain Ising, Box, and Associated integrals. The techniques we employ here include (a) the…
B. Ananthanarayan, Tanay Pathak, Kartik SharmaJan 31, 2023
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One-dimensional Discrete Dirac Operators in a Decaying Random Potential II: Clock, Schr\"odinger and Sine statistics
We consider one-dimensional discrete Dirac models in vanishing random environments. In a previous work [6], we showed that these models exhibit a rich phase diagram in terms of their spectrum as a…
Gregorio R. Moreno Flores, Amal TaarabtJan 30, 2023
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The density-density response function in time-dependent density functional theory: mathematical foundations and pole shifting
We establish existence and uniqueness of the solution to the Dyson equation for the density-density response function in time-dependent density functional theory (TDDFT) in the random phase…
Thiago Carvalho Corso, Mi-Song Dupuy, Gero FrieseckeJan 30, 2023
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Emergent Quasi-Bosonicity in Interacting Fermi Gases
This thesis concerns the correlation structure of interacting Fermi gases on a torus in the mean-field regime. A bosonization method in the spirit of Sawada is developed to analyze the system, and is…
Martin Ravn ChristiansenJan 30, 2023
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A Stochastic Differential Equation For Laser Propagation In Medias With Random Gaussian Absorption Coefficients: A Modified Beer's Law Solution Via A Van Kampen Cluster Expansion
Let I\!D=[0,L]⊂R+ be a slab geometry with boundaries z=0 and z=L. A laser beam with a flat incident intensity o enters the slab along the…
Steven D MillerJan 30, 2023
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Convergence of Quantum Lindstedt Series and Semiclassical Renormalization
In this work we consider the KAM renormalizability problem for small pseudodifferential perturbations of the semiclassical isochronous transport operator with Diophantine frequencies on the torus.…
Victor ArnaizJan 30, 2023
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Covariant Lyapunov vectors as global solutions of a partial differential equation on the phase space
As a new tool to describe the behaviour of a dynamical system, we introduce the concept of "covariant Lyapunov field", i.e. a field which assigns all the components of covariant Lyapunov vectors at…
Massimo Marino, Doriano BrogioliJan 29, 2023
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Towards integrable perturbation of 2d CFT on de Sitter space
We describe a procedure to deform the dynamics of a two-dimensional conformal net to possibly obtain a Haag-Kastler net on the de Sitter spacetime. The new dynamics is given by adding a primary field…
Christian D. Jäkel, Yoh TanimotoJan 29, 2023
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Wightman fields for two-dimensional conformal field theories with pointed representation category
Two-dimensional full conformal field theories have been studied in various mathematical frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our attention on theories…
Maria Stella Adamo, Luca Giorgetti, Yoh TanimotoJan 28, 2023
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Hydrodynamic and symbolic models of computation with advice
Dynamical systems and physical models defined on idealized continuous phase spaces are known to exhibit non-computable phenomena, examples include the wave equation, recurrent neural networks, or…
Robert CardonaJan 27, 2023
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A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity
The present work describes some extensions of an approach, originally developed by V.V. Yatsyk and the author, for the theoretical and numerical analysis of scattering and radiation effects on…
Lutz AngermannJan 27, 2023
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From particle systems to the BGK equation
In [Phys. Rev. 94 (1954), 511-525], P.L. Bhatnagar, E.P. Gross and M. Krook introduced a kinetic equation (the BGK equation), effective in physical situations where the Knudsen number is small…
Paolo Buttà, Mario Pulvirenti, Sergio SimonellaJan 27, 2023
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On dilation analyticity and spatial exponential decay of atomic ground states in non-relativistic qed
We consider the ground state and the ground state energy of an atom with spinless electrons in the framework of non-relativistic qed. We show that the ground state energy as well as the ground state…
David Hasler, Christian LejsekJan 27, 2023
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Exact solutions of Maxwell equations in homogeneous spaces with group of motions G3(IX)
The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group…
V. V. ObukhovJan 27, 2023
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Recursive characterisations of random matrix ensembles and associated combinatorial objects
We give an overview of the recursive characterisations of random matrix ensembles that are currently at the forefront of random matrix theory by way of studying two classes of ensembles using two…
Anas A. RahmanJan 26, 2023
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Perturbation determinant and Levinson's formula for Schr\"odinger operators with generalized point interaction
We consider the one dimensional Schr\"odinger operator with properly connecting generalized point interaction at the origin. We derive a trace formula for trace of difference of resolvents of…
M. Fazeel Anwar, Muhammad Usman, Muhammad Danish ZiaJan 26, 2023
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On the Thermodynamics of Particles Obeying Monotone Statistics
The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we…
Fabio Ciolli, Francesco Fidaleo, Chiara MarulloJan 26, 2023
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Non-existence of certain elliptic solutions of the Cubic-nonlinear Schr\"odinger Equation
For a certain class of solutions of the cubic nonlinear Sch\"odinger equation we prove non-existence in the generic case. In the nongeneric case we present a two-parameter set of solutions, bounded…
Hans Werner Schürmann, Valery SerovJan 26, 2023
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Quantum energy inequalities in integrable models with several particle species and bound states
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…
Henning Bostelmann, Daniela Cadamuro, Jan MandryschJan 25, 2023
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Non-homogeneous Hamiltonian structures for quasilinear systems
This paper aims at investigating necessary (and sufficient) conditions for quasilinear systems of first order PDEs to be Hamiltonian, with non-homogeneous operators of order 1 + 0, also with…
Pierandrea VergalloJan 25, 2023
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Self-adjointness of a class of multi-spin-boson models with ultraviolet divergences
We study a class of quantum Hamiltonian models describing a family of N two-level systems (spins) coupled with a structured boson field of positive mass, with a rotating-wave coupling mediated by…
Davide LonigroJan 25, 2023
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