Spin Networks, Wilson Loops and 3nj Wigner IdentitiesWe exploit the spin network properties of the magnetic eigenstates of SU(2) Hamiltonian lattice gauge theory and use the Wilson loop operators to obtain a wide class of new identities amongst 3nj…Manu Mathur, Atul Rathor·Nov 29, 2021SaveLearn
Study of small perturbations of a stationary state in a model of upper hybrid plasma oscillationsIt is shown that a constant external magnetic field, generally speaking, is not able to prevent breaking (loss of smoothness) of relativistic plasma oscillations, even if they are arbitrarily small…Olga S. Rozanova·Nov 29, 2021SaveLearn
Local Central Limit Theorem for Long-Range Two-Body Potentials at Sufficiently High TemperaturesDobrushin and Tirozzi [14] showed that, for a Gibbs measure with the finite-range potential, the Local Central Limit Theorem is implied by the Integral Central Limit Theorem. Campanino, Capocaccia,…Eric O. Endo, Vlad Margarint·Nov 28, 2021SaveLearn
The Harmonic Lagrange Top and the Confluent Heun EquationThe harmonic Lagrange top is the Lagrange top plus a quadratic (harmonic) potential term. We describe the top in the space fixed frame using a global description with a Poisson structure on T*S3.…Sean R. Dawson, Holger R. Dullin, Diana M. H. Nguyen·Nov 28, 2021SaveLearn
Propagation processes of correlations of hard spheresThe paper develops an approach to the description of the evolution of correlations for many hard spheres based on a hierarchy of evolution equations for the cumulants of the probability distribution…V. I. Gerasimenko, I. V. Gapyak·Nov 27, 2021SaveLearn
Validity of Bogoliubov's approximation for translation-invariant Bose gasesWe verify Bogoliubov's approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy EN is given by $EN=NeH+∈f…Morris Brooks, Robert Seiringer·Nov 27, 2021SaveLearn
Rate of Entropy Production in Stochastic Mechanical SystemsEntropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well…Gregory S. Chirikjian·Nov 27, 2021SaveLearn
Covariant influences for finite discrete dynamical systemsWe develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution.…Carlo Maria Scandolo, Gilad Gour, Barry C. Sanders·Nov 26, 2021SaveLearn
Perturbing Isoradial TriangulationsWe consider an infinite, planar, Delaunay graph which is obtained by locally deforming the embedding of a general, isoradial graph, w.r.t. a real deformation parameter ε. This entails a careful…Francois David, Jeanne Scott·Nov 26, 2021SaveLearn
Calogero type bounds in two dimensionsFor a Schrödinger operator on the plane R2 with electric potential V and Aharonov--Bohm magnetic field we obtain an upper bound on the number of its negative eigenvalues in terms of the…Ari Laptev, Larry Read, Lukas Schimmer·Nov 26, 2021SaveLearn
Semiheaps and Ternary Algebras in Quantum Mechanics RevisitedWe re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review the construction of a semiheap on a Hilbert space and the set of…Andrew James Bruce·Nov 26, 2021SaveLearn
Stationary scattering theory, the N-body long-range caseWithin the class of Dereziński-Enss pair-potentials which includes Coulomb potentials and for which asymptotic completeness is known De, we show that all entries of the N-body quantum…Erik Skibsted·Nov 25, 2021SaveLearn
Symmetries and Covariant Poisson brackets on pre-symplectic manifoldsNoticing that the space of the solutions of a first order Hamiltonian field theory has a pre-symplectic structure, we describe a class of conserved charges on it associated to the momentum map…Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort et al.·Nov 25, 2021SaveLearn
Index Theorems for One-dimensional Chirally Symmetric Quantum Walks with Asymptotically Periodic ParametersWe focus on index theory for chirally symmetric discrete-time quantum walks on the one-dimensional integer lattice. Such a discrete-time quantum walk model can be characterised as a pair of a unitary…Yasumichi Matsuzawa, Yohei Tanaka, Kazuyuki Wada·Nov 24, 2021SaveLearn
Large deviations for a binary collision model: energy evaporationWe analyze the large deviations for a discrete energy Kac-like walk. In particular, we exhibit a path, with probability exponentially small in the number of particles, that looses energy.Giada Basile, Dario Benedetto, Lorenzo Bertini et al.·Nov 24, 2021SaveLearn
Anisothermal Chemical Reactions: Onsager-Machlup and Macroscopic Fluctuation TheoryWe study a micro and macroscopic model for chemical reactions with feedback between reactions and temperature of the solute. The first result concerns the quasipotential as the large-deviation rate…D. R. Michiel Renger·Nov 23, 2021SaveLearn
Reducibility of 1-D Quantum Harmonic Oscillator with Decaying Conditions on the Derivative of Perturbation PotentialsWe prove the reducibility of 1-D quantum harmonic oscillators in R perturbed by a quasi-periodic in time potential V(x,ωt) under the following conditions, namely there is a C>0 such…Zhenguo Liang, Zhiqiang Wang·Nov 23, 2021SaveLearn
Reducibility of Quantum Harmonic Oscillator on Rd Perturbed by a Quasi-periodic Potential with Logarithmic DecayWe prove the reducibility of quantum harmonic oscillators in Rd perturbed by a quasi-periodic in time potential V(x,ωt) with logarithmic~decay. By a new estimate built for…Zhenguo Liang, Zhiqiang Wang·Nov 23, 2021SaveLearn
Modular structure of the Weyl algebraWe study the modular Hamiltonian associated with a Gaussian state on the Weyl algebra. We obtain necessary/sufficient criteria for the local equivalence of Gaussian states, independently of the…Roberto Longo·Nov 22, 2021SaveLearn
Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for coupled oscillators on simplicial complexesWe formulate a general Kuramoto model on weighted simplicial complexes where phases oscillators are supported on simplices of any order k. Crucially, we introduce linear and non-linear frustration…Alexis Arnaudon, Robert L. Peach, Giovanni Petri et al.·Nov 22, 2021SaveLearn
Many-body systems with SU(1,1) dynamical symmetry: from dynamics to thermodynamics based on the trace formulaFor a quantum (many-body) system with dynamical symmetry described by a given Lie group, we study the trace of exponential operators with complex coefficients in one of the irreducible subspaces in…Zhaoyu Fei, C. P. Sun·Nov 22, 2021SaveLearn
Heat Kernel, Spectral Functions and Anomalies in Weyl SemimetalsBeing motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary…A. V. Ivanov, M. A. Kurkov, D. V. Vassilevich·Nov 22, 2021SaveLearn
Generalized single-valued hyperlogarithmsSingle-valued hyperlogarithms are generalized to include primitives of differential forms d z/(azz+bz+cz+d), a,b,c,d∈C, where z is the…Oliver Schnetz·Nov 22, 2021SaveLearn
The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebrasThe main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type…Shanshan Liu, Abdenacer Makhlouf, Lina Song·Nov 22, 2021SaveLearn
Higher-order synchronization on the sphereWe construct a system of N interacting particles on the unit sphere Sd-1 in d-dimensional space, which has d-body interactions only. The equations have a gradient formulation derived from…M. A. Lohe·Nov 22, 2021SaveLearn