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Mathematical Physics papers — page 237

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Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional…
Farhang Loran, Ali MostafazadehMar 25, 2022
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Inverse Regge poles problem on a warped ball
In this paper, we study a new type of inverse problem on warped product Riemannian manifolds with connected boundary that we name warped balls. Using the symmetry of the geometry, we first define the…
Jack Borthwick, Nabile Boussaïd, Thierry DaudéMar 25, 2022
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Reduction and integrability: a geometric perspective
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor…
José F. CariñenaMar 25, 2022
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Quasilinear systems of first order PDEs with nonlocal Hamiltonian structures
In this paper we wonder whether a quasilinear system of PDEs of first order admits Hamiltonian formulation with local and nonlocal operators. By using the theory of differential coverings, we find…
Pierandrea VergalloMar 25, 2022
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Pickl's Proof of the Quantum Mean-Field Limit and Quantum Klimontovich Solutions
This paper discusses the mean-field limit for the quantum dynamics of N identical bosons in R3 interacting via a binary potential with Coulomb type singularity. Our approach is based on…
Immanuel Ben Porat, François GolseMar 24, 2022
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Adsorption of Lattice Polymers with Quenched Topologies
We introduce a framework for adsorption of a single polymer in which the topology of the polymer is quenched before adsorption, in contrast to more standard adsorption models having annealed…
Neal MadrasMar 24, 2022
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The inverse scattering transform for weak Wigner-von Neumann type potentials
In the context of the Cauchy problem for the Korteweg-de Vries equation we extend the inverse scattering transform to initial data that behave at plus infinity like a sum of Wigner-von Neumann type…
Sergei Grudsky, Alexei RybkinMar 24, 2022
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Infinite-dimensional Dubrovin-Frobenius manifolds and the Stokes phenomenon
We study the Dubrovin equation of the infinite-dimensional 2D Toda Dubrovin-Frobenius manifold at its irregular singularity. We first revisit the definition of the canonical coordinates, proving that…
Guido Carlet, Francisco Hernández IglesiasMar 24, 2022
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Improved Lieb-Oxford bound on the indirect and exchange energies
The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of N identical charges only in terms of their one-particle density. We prove here a new estimate on the…
Mathieu Lewin, Elliott H. Lieb, Robert SeiringerMar 23, 2022
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A general class of invariant diffusion processes in one dimension
This paper improves a previously established test involving only coefficients to decide a priori whether or not non-trivial symmetries of a large class of space-time dependent diffusion processes on…
F. GüngörMar 23, 2022
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Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation
In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf algebra structure on…
Yunnan Li, Yunhe Sheng, Rong TangMar 23, 2022
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A Generalized Method for the Darboux Transformation
A method is presented to obtain the change in the potential and in the relevant wavefunction of a linear system of ordinary differential equations containing a spectral parameter, when that linear…
Tuncay Aktosun, Mehmet UnluMar 23, 2022
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Analytical discrete ordinates for the three-dimensional radiative radiative equation in the half space
In one-dimensional transport theory, the method of analytical discrete ordinates (ADO) is known to be a concise and fast numerical scheme to solve the radiative transport equation. However, the…
Manabu MachidaMar 23, 2022
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A second order upper bound for the ground state energy of a hard-sphere gas in the Gross-Pitaevskii regime
We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius a/N, moving in the three-dimensional unit torus Λ. Our estimate captures…
Giulia Basti, Serena Cenatiempo, Alessandro Olgiati et al.Mar 22, 2022
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Multi-dimensional Jordan chain and Navier-Stokes Equation
Multi-dimensional Jordan chain is presented. It is shown that it admits the finite-component reductions to the Navier-Stokes equation and other important equations of continuous media theory.
B. G. KonopelchenkoMar 22, 2022
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Relation between spectra of Narain CFTs and properties of associated boolean functions
Recently, the construction of Narain CFT from a certain class of quantum error correcting codes has been discovered. In particular, the spectral gap of Narain CFT corresponds to the binary distance…
Yuma FurutaMar 22, 2022
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Mirror symmetry of height-periodic gradient Gibbs measures of a SOS model on Cayley trees
For the solid-on-solid (SOS) model with spin values from the set of all integers on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (which is an…
U. A. RozikovMar 22, 2022
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Linear superposition in the general heavenly equation
Evidently, the linear superposition principle can not be exactly established as a general principle in the presence of nonlinearity, and, at the first glance, there is no expectation for it to hold…
S. Y. Lou, Xiazhi HaoMar 22, 2022
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Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation
I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective theories,…
Niels BenedikterMar 21, 2022
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Cutting rules and positivity in finite temperature many-body theory
For a given diagrammatic approximation in many-body perturbation theory it is not guaranteed that positive observables, such as the density or the spectral function, retain their positivity. For…
Markku J. Hyrkäs, Daniel Karlsson, Robert van LeeuwenMar 21, 2022
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Bose gases in the Gross-Pitaevskii limit: a survey of some rigorous results
We review some mathematical work on the Bose gas in the Gross-Pitaevskii regime. We start with the classical results by Lieb, Seiringer and Yngvason on the ground state energy and by Lieb and…
Benjamin SchleinMar 21, 2022
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F-algebroids and deformation quantization via pre-Lie algebroids
In this paper, first we introduce a new approach to the notion of F-algebroids, which is a generalization of F-manifold algebras and F-manifolds, and show that F-algebroids are the…
John Alexander Cruz Morales, Jiefeng Liu, Yunhe ShengMar 21, 2022
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Unitary vertex algebras and Wightman conformal field theories
We prove an equivalence between the following notions: (i) unitary Möbius vertex algebras, and (ii) Wightman conformal field theories on the circle (with finite-dimensional conformal weight spaces)…
Christopher Raymond, Yoh Tanimoto, James E. TenerMar 21, 2022
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Topological Expansion of Oscillatory BGW and HCIZ Integrals at Strong Coupling
We prove that the BGW and HCIZ integrals admit large N topological expansions for complex coupling and complex external fields, provided the coupling is sufficiently strong. The expansion…
Jonathan NovakMar 21, 2022
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Hankel Determinant and Orthogonal Polynomials for a Perturbed Gaussian Weight: from Finite n to Large n Asymptotics
We study the monic polynomials orthogonal with respect to a symmetric perturbed Gaussian weight w(x;t):=e-x2(1+t\: x2)λ, x∈ R, where $t>…
Chao Min, Yang ChenMar 20, 2022
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