Temporal Entropy Evolution in Stochastic and Delayed DynamicsWe review the behaviour of the Gibbs' and conditional entropies in deterministic and stochastic systems and continue to a formulation appropriate for a stochastically perturbed system with delayed…Michael C. Mackey, Marta Tyran-Kaminska·Nov 28, 2023SaveLearn
On variable-order fractional linear viscoelasticityWe discuss a generalisation of fractional linear viscoelasticity based on Scarpi's approach to variable-order fractional calculus. After reviewing the general mathematical framework, we introduce the…A. Giusti, I. Colombaro, R. Garra et al.·Nov 27, 2023SaveLearn
Principal Landau DeterminantsWe reformulate the Landau analysis of Feynman integrals with the aim of advancing the state of the art in modern particle-physics computations. We contribute new algorithms for computing Landau…Claudia Fevola, Sebastian Mizera, Simon Telen·Nov 27, 2023SaveLearn
On Dynamics and Thermodynamics of Moving MediaIn this paper recent results regarding generalized continuum mechanics on oriented Riemannian manifolds are reviewed and summarized. The mass, the momentum and the energy conservation laws are given.…Anna Duyunova, Valentin Lychagin, Sergey Tychkov·Nov 27, 2023SaveLearn
The Geometry of the solution space of first order Hamiltonian field theories III: Palatini's formulation of General RelativityWe complete the program started in two companion papers of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamiltonian field theories. The…Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort et al.·Nov 27, 2023SaveLearn
The inverse problem within free Electrodynamics and the coisotropic embedding theoremWe present the coisotropic embedding theorem as a tool to provide a solution for the inverse problem of the calculus of variations for a particular class of implicit differential equations, namely…Luca Schiavone·Nov 27, 2023SaveLearn
Generalized cycles on Spectral CurvesGeneralized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in…B. Eynard·Nov 26, 2023SaveLearn
Asymmetric Bethe AnsatzThe recently proposed exact quantum solution for two δ-function-interacting particles with a mass-ratio 3\!:\!1 in a hard-wall box [Y. Liu, F. Qi, Y. Zhang and S. Chen, iScience 22, 181…Steven G. Jackson, Hélène Perrin, Gregory E. Astrakharchik et al.·Nov 26, 2023SaveLearn
General O(D)-equivariant fuzzy hyperspheres via confining potentials and energy cutoffsWe summarize our recent construction of new fuzzy hyperspheres Sd of arbitrary dimension d covariant under the full orthogonal group O(D), D=d+1. We impose a suitable energy…Gaetano Fiore·Nov 25, 2023SaveLearn
An energy-momentum method for ordinary differential equations with an underlying k-polysymplectic manifoldThis work presents a comprehensive review of the k-polysymplectic Marsden-Weinstein reduction theory, rectifying prior errors and inaccuracies in the literature while introducing novel findings. It…Leonardo Colombo, Javier de Lucas, Xavier Rivas et al.·Nov 25, 2023SaveLearn
On the integration of Ito equations with a random or a W-symmetrySymmetries can be used to integrate scalar Ito equation -- or reduce systems of such equations -- by the Kozlov substitution, i.e. passing to symmetry adapted coordinates. While the theory is well…Giuseppe Gaeta·Nov 25, 2023SaveLearn
An exact solution for the magnetic diffusion problem with a step-function resistivity modelIn the magnetic diffusion problem, a magnetic diffusion equation is coupled by an Ohmic heating energy equation. The Ohmic heating can make the magnetic diffusion coefficient (i. e., the resistivity)…Bo Xiao, Ganghua Wang, Li Zhao et al.·Nov 25, 2023SaveLearn
Twisted Araki-Woods Algebras, the Yang-Baxter Equation, and quantum field theoryThis article reviews recent work with Correa da Silva on twisted Araki-Woods algebras, including an introduction to twisted Fock spaces and standard subspaces. We discuss a new family of examples of…Gandalf Lechner·Nov 24, 2023SaveLearn
A master-slave coupling scheme for synchronization and parameter estimation in the generalized Kuramoto-Sivashinsky equationThe problem of estimating the constant parameters of the Kuramoto-Sivashinsky (KS) equation from observed data has received attention from researchers in physics, applied mathematics and statistics.…Joaquin Miguez, Harold Molina-Bulla, Inés P. Mariño·Nov 23, 2023SaveLearn
Geometric aspects of a spin chainWe discuss non-equilibrium thermodynamics of the mean field Ising model from a geometric perspective, focusing on the thermodynamic limit. When the number of spins is finite, the Gibbs equilibria…Michael Entov, Leonid Polterovich, Lenya Ryzhik·Nov 23, 2023SaveLearn
Slow propagation of information on the random XXZ quantum spin chainThe random XXZ quantum spin chain manifests localization (in the form of quasi-locality) in any fixed energy interval, as previously proved by the authors. In this article it is shown that this…Alexander Elgart, Abel Klein·Nov 23, 2023SaveLearn
Algebrodynamics: Shear-Free Null Congruences and New Types of Electromagnetic FieldsWe briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions ( B) in particular. We demonstrate that any B-differentiable function…Vladimir V. Kassandrov, Joseph A. Rizcallah, Ivan A. Matveev·Nov 23, 2023SaveLearn
Semiclassical analysis of two-scale electronic Hamiltonians for twisted bilayer grapheneThis paper investigates the mathematical properties of independent-electron models for twisted bilayer graphene by examining the density-of-states of corresponding single-particle Hamiltonians using…Eric Cancès, Long Meng·Nov 23, 2023SaveLearn
From each of Feynman's and von Neumann's postulates to the restricted Feynman path integrals: a mathematical theory of temporally continuous quantum measurementsFeynman proposed a postulate or a method of quantization in his celebrated paper in 1948. Applying Feynman's postulate to temporally continuous quantum measurements of the positions of particles,…Wataru Ichinose·Nov 23, 2023SaveLearn
Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metricsWe study algebraic and projective geometric properties of Hamiltonian trios determined by a constant coefficient second-order operator and two first-order localizable operators of Ferapontov type. We…P. Lorenzoni, R. Vitolo·Nov 23, 2023SaveLearn
Comments on mathematical aspects of the Bir\'o-N\'eda modelWe address two mathematical aspects of the Bir\'o--N\'eda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit…Ilda Inácio, José Velhinho·Nov 22, 2023SaveLearn
Wick-type deformation quantization of contact metric manifoldsWe construct a Wick-type deformation quantization of contact metric manifolds. The construction is fully canonical and involves no arbitrary choice. Unlike the case of symplectic or Poisson…Boris M. Elfimov, Alexey A. Sharapov·Nov 21, 2023SaveLearn
Nonlocal PDEs and quantum optics: band structure of periodic atomic sytemsWe continue our study of the quantum optics of a single photon interacting with a system of two level atoms. In this work we investigate the case of a periodic arrangement of atoms. We provide a…Erik Orvehed Hiltunen, Joseph Kraisler, John C. Schotland et al.·Nov 21, 2023SaveLearn
-Minkowski as tangent space I: quantum partition of unityWe define a quantum (noncommutative) analogue of locally trivial tangent bundle based on two main elements: the definition of local algebras through quotients of ideals of the global algebra as…Kilian Hersent, Jean-Christophe Wallet·Nov 21, 2023SaveLearn
On anomalous diffusion in the Kraichnan model and correlated-in-time variantsWe provide a concise PDE-based proof of anomalous diffusion in the Kraichan model -- a stochastic, white-in-time model of passive scalar turbulence. That is, we show an exponential rate of L2…Keefer Rowan·Nov 20, 2023SaveLearn