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Mathematical Physics papers — page 203

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Homotopy of periodic two by two matrices
We describe the homotopy classes of 2 by 2 periodic simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in three…
Joseph E. Avron, Ari M. TurnerDec 14, 2022
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A quantum energy inequality in the Sine--Gordon model
We consider the stress tensor in the massless Sine--Gordon model in the finite regime β2 < 4 π of the theory. We prove convergence of the renormalised perturbative series for the interacting…
Markus B. Fröb, Daniela CadamuroDec 14, 2022
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A Metric Graph for Which the Number of Possible Endpoints of a Random Walk Grows Minimally
We prove that metric graph with the minimal growth of the number of possible endpoints of a random walk is the union of several linear paths coming out of the same vertex
V. L. Chernyshev, A. A. TolchennikovDec 13, 2022
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Symmetry analysis and hidden variational structure of Westervelt's equation in nonlinear acoustics
Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-sound in human…
Stephen C. Anco, Almudena P. Marquez, Tamara M. Garrido et al.Dec 13, 2022
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C*-algebraic results in the search for quantum gauge fields
This thesis consists of two parts, both situated in operator theory, and both motivated by the quest for rigorous quantizations of gauge theories. The first part is based on [Skripka,vN - JST 2022],…
Teun D. H. van NulandDec 13, 2022
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Infinite-dimensional genetic and evolution algebras generated by Gibbs measures
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical…
Cristian F. Coletti, Lucas R. de Lima, Denis A. LuizDec 13, 2022
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Solving the n-color ice model
Given an arbitrary choice of two sets of nonzero Boltzmann weights for n-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e.,…
Patrick Addona, Ethan Bockenhauer, Ben Brubaker et al.Dec 13, 2022
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Interface currents and corner states in magnetic quarter-plane systems
We study the propagation of currents along the interface of two 2-d magnetic systems, where one of them occupies the first quadrant of the plane. By considering the tight-binding approximation…
Danilo Polo OjitoDec 12, 2022
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Fractional Dirac Equations from Polynomial Linearization: Solutions and Difficulties
The linearization of a quadratic form gives rise to a Clifford algebra structure, as seen in Dirac's factorization of the d'Alembert operator. A similar structure known as a generalized Clifford…
Erin T. Albertin, Zachary P. Bradshaw, Kaitlyn M. Kirt et al.Dec 12, 2022
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Hierarchies in relative Picard-Lefschetz theory
We prove a relative version of the Picard-Lefschetz theorem, describing the variation of relative homology groups Hd(Yt At,Bt At) in the fibers of a smooth fiber bundle $Y…
Marko Berghoff, Erik PanzerDec 12, 2022
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Avila's acceleration via zeros of determinants, and applications to Schr\"odinger cocycles
In this paper we give a characterization of Avila's quantized acceleration of the Lyapunov exponent via the number of zeros of the Dirichlet determinants in finite volume. As applications, we prove…
Rui Han, Wilhelm SchlagDec 12, 2022
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Some Mixed-Moments of Gaussian Elliptic Matrices and Ginibre Matrices
We consider the mixed-moments $(Xε1,…,Xεk)=N∞N-1E[Tr(Xε1·sXεk…
Théo DessertaineDec 12, 2022
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Extension of Realisations for Low-Dimensional Lie Algebras and Relative Differential Invariants
We start with a realisation of a Lie algebra with the basis operators L= Qm, Qm=ζmj(xi)∂xj, where xi are some variables that may be regarded as dependent or…
Iryna YehorchenkoDec 12, 2022
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Family of nonstandard integrable and superintegrable classical Hamiltonian systems in non-vanishing magnetic fields
In this paper we present the construction of all nonstandard integrable systems in magnetic fields whose integrals have leading order structure corresponding to the case (i) of Theorem 1 in [A…
Md Fazlul Hoque, Libor ŠnoblDec 10, 2022
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Double Dirac cones in band structures of periodic Schr\"odinger operators
Dirac cones are conical singularities that occur near the degenerate points in band structures. Such singularities result in enormous unusual phenomena of the corresponding physical systems. This…
Ying Cao, Yi ZhuDec 10, 2022
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A survey on deformations, cohomologies and homotopies of relative Rota-Baxter Lie algebras
In this paper, we review deformation, cohomology and homotopy theories of relative Rota-Baxter Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived…
Yunhe ShengDec 9, 2022
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Hamiltonian representation of isomonodromic deformations of general rational connections on gl2(C)
In this paper, we study and build the Hamiltonian system attached to any gl2(C) meromorphic connection with an arbitrary number of non-ramified poles of arbitrary degrees. In…
Olivier Marchal, Nicolas Orantin, Mohamad AlameddineDec 9, 2022
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Higher Chern-Simons based on (2-)crossed modules
We present higher Chern-Simons theories based on (2-)crossed modules. We start from the generalized differential forms in Generalized Differential Calculus and define the corresponding generalized…
Danhua Song, Mengyao Wu, Ke Wu et al.Dec 9, 2022
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Upper bound for the ground state energy of a dilute Bose gas of hard spheres
We consider a gas of bosons interacting through a hard-sphere potential with radius a in the thermodynamic limit. We derive a simple upper bound for the ground state energy per particle at…
Giulia Basti, Serena Cenatiempo, Alessandro Giuliani et al.Dec 8, 2022
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Tunneling effect in two dimensions with vanishing magnetic fields
In this paper, we consider the semiclassical 2D magnetic Schr\"odinger operator in the case where the magnetic field vanishes along a smooth closed curve. Assuming that this curve has an axis of…
Khaled Abou AlfaDec 8, 2022
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A new formula for intersection numbers
We propose a new formula to compute Witten--Kontsevich intersection numbers. It is a closed formula, not involving recursion neither solving equations. It only involves sums over partitions of…
Bertrand Eynard, Dimitrios MitsiosDec 8, 2022
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Cylindrical first order superintegrability with complex magnetic fields
This article is a contribution to the study of superintegrable Hamiltonian systems with magnetic fields on the three-dimensional Euclidean space E3 in quantum mechanics. In contrast to…
Ondřej Kubů, Libor ŠnoblDec 8, 2022
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Virtual Euler characteristics via topological recursion
We use Seiberg--Witten-like relations in the topological recursion framework to obtain virtual Euler characteristics for uni- and multicellular maps for ensembles of classic orthogonal polynomials…
Leonid O. ChekhovDec 8, 2022
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Multiple Landau level filling for a mean field limit of 2D fermions
Motivated by the quantum hall effect, we study N two dimensional interacting fermions in a large magnetic field limit. We work in a bounded domain, ensuring finite degeneracy of the Landau levels. In…
Denis PériceDec 7, 2022
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De Rham - Witt KZ equations
We propose a de Rham - Witt version of the derived Knizhnik-Zamolodchikov equations, and of their hypergeometric realizations. We also propose de Rham - Witt versions of some classical theorems…
Vadim Schechtman, Alexander VarchenkoDec 7, 2022
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