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Mathematical Physics papers — page 166

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On the interplay between vortices and harmonic flows: Hodge decomposition of Euler's equations in 2d
Let be a compact manifold without boundary whose first homology is nontrivial. Hodge decomposition of the incompressible Euler's equation in terms of 1-forms yields a coupled PDE-ODE system.…
Clodoaldo Grotta-Ragazzo, Björn Gustafsson, Jair KoillerSep 22, 2023
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Global and Local Nilpotent Bases of Matrices
In studying the unusual properties of a special Witt basis of a Clifford geometric algebra with a Lorentz metric, a new concept of local duality makes it possible to define any real geometric algebra…
Garret SobczykSep 21, 2023
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Six-Vertex Model and Random Matrix Distributions
We survey the connections between the six-vertex (square ice) model of 2d statistical mechanics and random matrix theory. We highlight the same universal probability distributions appearing on both…
Vadim Gorin, Matthew NicolettiSep 21, 2023
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A rigorous model reduction for the anisotropic-scattering transport process
In this letter, we propose a reduced-order model to bridge the particle transport mechanics and the macroscopic fluid dynamics in the highly scattered regime. A rigorous mathematical derivation and a…
Yuan Hu, Chang Liu, Huayun ShenSep 21, 2023
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A generalization of the Witten conjecture through spectral curve
We propose a generalization of the Witten conjecture, which connects a descendent enumerative theory with a specific reduction of KP integrable hierarchy. Our conjecture is realized by two parts:…
Shuai Guo, Ce Ji, Qingsheng ZhangSep 21, 2023
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Ground state of Bose gases interacting through singular potentials
We consider a system of N bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form N3β-1 v (Nβ x) for β ∈ (0,1). We…
Lea Boßmann, Nikolai Leopold, Sören Petrat et al.Sep 21, 2023
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KP integrability through the x-y swap relation
We discuss a universal relation that we call the x-y swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in…
Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski et al.Sep 21, 2023
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Cohomological Lagrangian field theory
This paper introduces a geometric framework for classical cohomological field theories based on G-algebras and gauge natural field theories. A BV-BFV extension of the framework is provided,…
Shuhan JiangSep 21, 2023
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Discrete Spinning Tops -- Difference equations for Euler, Lagrange, and Kowalevski tops
Several methods of time discretization are examined for integrable rigid body models, such as Euler, Lagrange, and Kowalevski tops. Problems of Lax-Moser pairs, conservation laws, and explicit solver…
Kiyoshi SogoSep 21, 2023
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Bethe ansatz solutions and hidden sl(2) algebraic structure for a class of quasi-exactly solvable systems
The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the…
Siyu Li, Ian Marquette, Yao-Zhong ZhangSep 21, 2023
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Almost-Poisson brackets for nonholonomic systems with gyroscopic terms and Hamiltonisation
We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the…
L. C. García-Naranjo, J. C. Marrero, D. Martín de Diego et al.Sep 20, 2023
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Rational extensions of an oscillator-shaped quantum well potential in a position-dependent mass background
We show that a recently proposed oscillator-shaped quantum well model associated with a position-dependent mass can be solved by applying a point canonical transformation to the constant-mass…
C. QuesneSep 20, 2023
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Algebraic structures and Hamiltonians from the equivalence classes of 2D conformal algebras
The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions rely on explicit…
Ian Marquette, Junze Zhang, Yao-Zhong ZhangSep 20, 2023
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Principal hierarchy of Infinite-dimensional Frobenius Manifold Underlying the Extended Kadomtsev-Petviashvili Hierarchy
In this paper, we construct the principal hierarchy of the infinite-dimensional Frobenius manifold underlying the extended Kadomtsev-Petviashvili hierarchy. We show that this hierarchy serves as an…
Shilin MaSep 19, 2023
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Wm-algebras and fractional powers of difference operators
In this paper we describe a Poisson pencil associated to the lattice Wm-algebras defined in IM, and we prove that the Poisson pencil is equal to the one defined in MW and CM…
Gloria Marí BeffaSep 18, 2023
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Relativistic Propagators on Lattices
I define the lattice propagator on a very general collection of graphs, namely graphs locally isomorphic to Zd× Z. I then define polygonal approximations to the minkowski…
Rory O'DwyerSep 18, 2023
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Moving Frames: Difference and Differential-Difference Lagrangians
This paper develops moving frame theory for partial difference equations and for differential-difference equations with one continuous independent variable. In each case, the theory is applied to the…
Lewis C. White, Peter E. HydonSep 16, 2023
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Solitons and Normal Random Matrices
We discuss a general relation between the solitons and statistical mechanics and show that the partition function of the normal random matrix model can be obtained from the multi-soliton solutions of…
I. M. Loutsenko, V. P. Spiridonov, O. V. YermolayevaSep 16, 2023
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Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions
In this proceeding we consider a translation invariant Nelson type model in two spatial dimensions modeling a scalar relativistic particle in interaction with a massive radiation field. As is…
Benjamin Hinrichs, Oliver MatteSep 16, 2023
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Symplectic and Lagrangian Polar Duality; Applications to Quantum Information Geometry
Polar duality is a well-known concept from convex geometry and analysis. In the present paper, we study two symplectically covariant versions of polar duality keeping in mind their applications to…
Maurice de Gosson, Charlyne de GossonSep 14, 2023
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A single layer representation of the scattered field for multiple scattering problems
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers.…
Didier Felbacq, Anthony Gourdin, Emmanuel RousseauSep 14, 2023
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Central limit theorem for the random variables associated with the IDS of the Anderson model on lattice
We consider the existence of the integrated density of states (IDS) of the Anderson model on the Hilbert space 2(Zd) as analogues to the law of large numbers (LLN). In this work, we…
Dhriti Ranjan DolaiSep 14, 2023
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Geometric Derivation of the Finite N Master Loop Equation
In this paper we provide a geometric derivation of the master loop equation for the lattice Yang-Mills model with structure group G ∈ \SO(N),SU(N), U(N)\. This approach is based on integration…
Omar Abdelghani, Ron NissimSep 14, 2023
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Transcendental properties of entropy-constrained sets: Part II
In this work, we address the question of the impossibility of certain single-letter formulas by exploiting the semi-algebraic nature of various entropy-constrained sets. The focus lies on studying…
Vjosa Blakaj, Chokri ManaiSep 14, 2023
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Local versus global subtleties of projective representations
In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously,…
J. M. Hoff da Silva, J. E. RodriguesSep 13, 2023
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