Non-unique Hamiltonians for Discrete Symplectic DynamicsAn outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory…Liyan Ni, Yihao Zhao, Zhonghan Hu·May 13, 2024SaveLearn
On the equivalence between n-state spin and vertex models on the square latticeIn this paper we investigate a correspondence among spin and vertex models with the same number of local states on the square lattice with toroidal boundary conditions. We argue that the partition…M. J. Martins·May 12, 2024SaveLearn
Restricted isometric compression of sparse datasets into low-dimensional varietiesThis article extends the known restricted isometric projection of sparse datasets in Euclidean spaces RN down into low-dimensional subspaces Rk, k N, to the case of…Vasile Pop, Iuliana Teodorescu, Razvan Teodorescu·May 10, 2024SaveLearn
Projective connections and extremal domains for analytic contentThis note expands on the recent proof ABKT that the extremal domains for analytic content in two dimensions can only be disks and annuli. This result's unexpected implication for theoretical…Razvan Teodorescu·May 10, 2024SaveLearn
Integrability-preserving regularizations of Laplacian GrowthThe Laplacian Growth (LG) model is known as a universality class of scale-free aggregation models in two dimensions, characterized by classical integrability and featuring finite-time boundary…Razvan Teodorescu·May 10, 2024SaveLearn
New Procedure for Evaluation of U(3) Coupling and Recoupling CoefficientsA simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group-subgroup chains is presented. While the canonical U(3)->U(2)->U(1) coupling and…Phong Dang, Jerry P. Draayer, Feng Pan et al.·May 10, 2024SaveLearn
A touch of quantum field theoryThe overlap of Srinivasa Ramanujan's work with quantum field theory is discussed. A mathematically natural axiom for euclidean quantum field theories is proposed.Werner Nahm·May 9, 2024SaveLearn
Meta Algebras and Biorthogonal Rational Functions: The Hahn CaseThe finite families of biorthogonal rational functions and orthogonal polynomials of Hahn type are interpreted algebraically in a unified way by considering the three-generated meta Hahn algebra and…Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov·May 9, 2024SaveLearn
Twisting factors and fixed-time models in quantum field theoryWe construct a class of fixed-time models in which the commutations relations of a Dirac field with a bosonic field are non-trivial and depend on the choice of a given distribution ("twisting…Ezio Vasselli·May 9, 2024SaveLearn
Radiative corrections to the dynamics of a tracer particle coupled to a Bose scalar fieldWe consider a tracer particle coupled to a Bose scalar field and study the regime where the field's propagation speed approaches infinity. For initial states devoid of field excitations, we introduce…Esteban Cárdenas, David Mitrouskas·May 8, 2024SaveLearn
Classical Grand Angular Momentum in N-Body ProblemsThe concept of grand angular momentum is widely used in the study of N-body problems quantum mechanically. Here, we applied it to a classical analysis of N-body problems. Utilizing the tree…Zhongqi Liang, Jesús Pérez-Ríos·May 8, 2024SaveLearn
Generalized vector potential and Trace Theorem for Lipschitz domainsThe vector potential is a fundamental concept widely applied across various fields. This paper presents an existence theorem of a vector potential for divergence-free functions in…Zhen Liu, Jinbiao Wu·May 8, 2024SaveLearn
Large N limit of fuzzy geometries coupled to fermionsIn this paper we present an analysis of the large N limit of a family of quartic Dirac ensembles based on (0, 1) fuzzy geometries that are coupled to fermions. These Dirac ensembles are examples of…Masoud Khalkhali, Nathan Pagliaroli, Luuk S. Verhoeven·May 8, 2024SaveLearn
Tube Formulae for Generalized von Koch Fractals through Scaling Functional EquationsIn this work, we provide a treatment of scaling functional equations in a general setting involving fractals arising from sufficiently nice self-similar systems in order to analyze the tube…Will Hoffer·May 7, 2024SaveLearn
Multicomplex Ideals, Modules and Hilbert SpacesIn this article we study some algebraic aspects of multicomplex numbers Mn. For n≥ 2 a canonical representation is defined in terms of the multiplication of n-1 idempotent elements.…Derek Courchesne, Sébastien Tremblay·May 7, 2024SaveLearn
Symmetry-enhanced Lieb-Robinson bounds for a class of Bose-Hubbard type HamiltoniansSeveral recent works have derived Lieb-Robinson bounds (LRBs) for Bose-Hubbard-type Hamiltonians. For certain structured initial states, e.g., vacuum perturbations or near-stationary states,…Tomotaka Kuwahara, Marius Lemm·May 7, 2024SaveLearn
Diatomic Molecules in deSitter and Anti-deSitter SpacesThe Schr\"odinger equation for diatomic molecules in deSitter and anti-deSitter spaces is studied using the extended uncertainty principle formulation. The equations are solved by the…Meriem AbdelAziz, Mustafa Moumni, Mokhtar Falek·May 7, 2024SaveLearn
Analyticity for locally stable hard-core gases via recursionIn their recent works [Comm. Math. Phys. 399:1 (2023)] and [arXiv:2109.01094], Michelen and Perkins proved that the pressure of a system of particles with repulsive pair interactions is analytic for…Qidong He·May 7, 2024SaveLearn
Brownian Motion on The Spider Like Quantum GraphsThe paper contains the probabilistic analysis of the Brownian motion on the simplest quantum graph, spider: a system of N-half axis connected only at the graph's origin by the simplest (so-called…Madhumita Paul, Stanislav Molchanov·May 7, 2024SaveLearn
Evaluation of integrals for the emptiness formation probability in the square-ice modelWe study the emptiness formation probability (EFP) in the six-vertex model with domain wall boundary conditions. We present a conjecture according to which at the ice point, i.e., when all the…Filippo Colomo, Andrei G. Pronko·May 7, 2024SaveLearn
Darboux's Theorem, Lie series and the standardization of the Salerno and Ablowitz-Ladik modelsIn the framework of nonlinear Hamiltonian lattices, we revisit the proof of Moser-Darboux's Theorem, in order to present a general scheme for its constructive applicability to Hamiltonian models with…Marco Calabrese, Simone Paleari, Tiziano Penati·May 7, 2024SaveLearn
Parametric set-theoretic Yang-Baxter equation: p-racks, solutions & quantum algebrasThe theory of the parametric set-theoretic Yang-Baxter equation is established from a purely algebraic point of view. The first step towards this objective is the introduction of certain…Anastasia Doikou·May 7, 2024SaveLearn
Expansion of the Many-body Quantum Gibbs State of the Bose-Hubbard Model on a Finite GraphWe consider the many-body quantum Gibbs state for the Bose-Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, corresponding to a…Zied Ammari, Shahnaz Farhat, Sören Petrat·May 7, 2024SaveLearn
Twisted vortices in two-component Ginzburg-Landau theoryIn this note, a brief introduction to the physical and mathematical background of the two-component Ginzburg-Landau theory is given. From this theory we derive a boundary value problem whose solution…Lei Cao, Shouxin Chen·May 7, 2024SaveLearn
Learning the local density of states of a bilayer moir\'e material in one dimensionRecent work of three of the authors showed that the operator which maps the local density of states of a one-dimensional untwisted bilayer material to the local density of states of the same bilayer…Diyi Liu, Alexander B. Watson, Michael Hott et al.·May 6, 2024SaveLearn