Interaction spaces: towards a universal mathematical theory of complex systemsWe present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models,…Paolo Giordano·Jul 2, 2024SaveLearn
On the uniqueness of the strictly convex quadrilateral central configuration with a fixed angleThe conjecture of the existence and the uniqueness of the strictly convex quadrilateral central configuration for the Newtonian 4-body problem is one of the most-talked open problems in the study of…Yangshanshan Liu, Shiqing Zhang·Jul 2, 2024SaveLearn
Field Theories on Quantum Space-Times: Towards the Phenomenology of Quantum GravityNoncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry,…Kilian Hersent·Jul 2, 2024SaveLearn
Localization for Lipschitz monotone quasi-periodic Schr\"odinger operators on Zd via Rellich functions analysisWe establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schr\"odinger operators on Zd with bounded or unbounded Lipschitz monotone…Hongyi Cao, Yunfeng Shi, Zhifei Zhang·Jul 2, 2024SaveLearn
Lie-Hamilton systems on Riemannian and Lorentzian spaces from conformal transformations and some of their applicationsWe propose a generalization of two classes of Lie-Hamilton systems on the Euclidean plane to two-dimensional curved spaces, leading to novel Lie-Hamilton systems on Riemannian spaces (flat 2-torus,…Rutwig Campoamor-Stursberg, Oscar Carballal, Francisco J. Herranz·Jul 1, 2024SaveLearn
Triviality proof for mean-field 44-theoriesThe differential equations of the Wilson renormalization group are a powerful tool to study the Schwinger functions of Euclidean quantum field theory. In particular renormalization theory can be…Pierre Wang, Christoph Kopper·Jul 1, 2024SaveLearn
Representations of quadratic Heisenberg-Weyl algebras and polynomials in the fourth Painlev\'e transcendentWe provide new insights into the solvability property of an Hamiltonian involving of the fourth Painlev\'e transcendent and its derivatives. This Hamiltonian is third order shape invariant and can…Ian Marquette·Jul 1, 2024SaveLearn
Spin chain techniques for angular momentum quasicharactersWe study the ring of invariant functions over the N-fold Cartesian product of copies of the compact Lie group G=SU(2), modulo the action of conjugation by the diagonal subgroup, generalizing the…P D Jarvis, G Rudolph·Jul 1, 2024SaveLearn
Linear Criterion for an Upper Bound on the Bardeen-Cooper-Schrieffer Critical TemperatureSince Bardeen-Cooper-Schrieffer theory of superconductivity is non-linear, it is difficult to study superconducting properties analytically. There is a more tractable linear criterion which…Barbara Roos·Jun 30, 2024SaveLearn
Circular symmetry-breaking and topological Noether currentsWe propose a toy model for the algebraic topology of bubbling as circular symmetry-breaking, in terms of asymptotic expressions for Noether currents and cobordism of manifolds with circle actions…Jack Morava·Jun 30, 2024SaveLearn
Abstract ladder operators for non self-adjoint Hamiltonians, with applicationsLadder operators are useful, if not essential, in the analysis of some given physical system since they can be used to find easily eigenvalues and eigenvectors of its Hamiltonian. In this paper we…Fabio Bagarello·Jun 30, 2024SaveLearn
Gauge Fixing in QFT and the Dressing Field MethodIn this paper, we revisit the Dressing Field Method (DFM) in the context of Quantum (Gauge) Field Theories (QFT). In order to adapt this method to the functional path integral formalism of QFT, we…Mathilde Guillaud, Serge Lazzarini, Thierry Masson·Jun 28, 2024SaveLearn
Second order energy expansion of Bose gases with three-body interactionsWe provide a second order energy expansion for a gas of N bosonic particles with three-body interactions in the Gross-Pitaevskii regime. We especially confirm a conjecture by Nam, Ricaud and Triay…Morris Brooks·Jun 28, 2024SaveLearn
Reflection operator and hypergeometry II: SL(2, C) spin chainWe consider noncompact open SL(2, C) spin chain and construct eigenfunctions of B-element of monodromy matrix for the simplest case of the chain with one site. The reflection operator…P. Antonenko, N. Belousov, S. Derkachov et al.·Jun 28, 2024SaveLearn
Reflection operator and hypergeometry I: SL(2, R) spin chainIn this work we consider open SL(2, R) spin chain, mainly the simplest case of one particle. Eigenfunctions of the model can be constructed using the so-called reflection operator. We…P. Antonenko, N. Belousov, S. Derkachov et al.·Jun 28, 2024SaveLearn
Periodicity of atomic structure in a Thomas-Fermi mean-field modelWe consider a Thomas-Fermi mean-field model for large neutral atoms. That is, Schr\"odinger operators HZTF=--ZTF in three-dimensional space, where Z is the nuclear…August Bjerg, Jan Philip Solovej·Jun 28, 2024SaveLearn
Many-body Fu-Kane-Mele indexWe define a Z2-valued index for stably short-range entangled states of two-dimensional fermionic lattice systems with charge conservation and time reversal symmetry. The index takes its…Sven Bachmann, Alex Bols, Mahsa Rahnama·Jun 27, 2024SaveLearn
Modular Hamiltonian and modular flow of massless fermions on a cylinderWe determine explicitly the modular flow and the modular Hamiltonian for massless free fermions in diamonds on a cylinder in 1+1 dimensions. We consider both periodic and antiperiodic boundary…Daniela Cadamuro, Markus B. Fröb, Guillem Pérez-Nadal·Jun 27, 2024SaveLearn
Towards 2-dimensional non-commutative integralsWe collect evidence that the notion of path-ordered non-abelian integration admits an extension to two dimensions. We propose the corresponding notion of non-abelian 2-form along the lines of Lie…Pavel Suprun·Jun 27, 2024SaveLearn
Explicit Hamiltonian representations of meromorphic connections and duality from different perspectives: a case studyIn this article, we present an explicit study of -deformed meromorphic connections in gl3(C) with an unramified irregular pole at infinity of order r∞=3 and its…Mohamad Alameddine, Olivier Marchal·Jun 27, 2024SaveLearn
A Novel Generalisation of Supersymmetry: Quantum Z22-Oscillators and their `superisation'We propose a very simple toy model of a Z22-supersymmetric quantum system and show, via Klein's construction, how to understand the system as being an N=2 supersymmetric system with an…Andrew James Bruce·Jun 27, 2024SaveLearn
Optimal version of the fundamental theorem of chronogeometryWe study lightlikeness preserving mappings from the 4-dimensional Minkowski spacetime M4 to itself under no additional regularity assumptions like continuity, surjectivity, or…Michiya Mori, Peter Šemrl·Jun 27, 2024SaveLearn
Local aspects of topological quantization and the Wu-Yang MonopolesIn this paper, we review how local potentials arise in the Wu-Yang topological quantization. We also discuss the isomorphism between the de Rham cohomology classes and Cech cohomology classes in such…Aayush Verma·Jun 27, 2024SaveLearn
Thermodynamics of Viscous Flows on SurfacesIn this paper, thermodynamics of a moving medium is considered. Main goal of this paper is to describe thermodynamics state equations and equations of co-existence manifolds of media on two- and…Anna Duyunova, Valentin Lychagin, Sergey Tychkov·Jun 26, 2024SaveLearn
A Mathematical Aspect of Bloch's TheoremIn this paper, by studying a class of 1-D Sturm-Liouville problems with periodic coefficients, we show and classify the solutions of periodic Schrodinger equations in a multidimensional case, which…Yan Li, Bin Yang, Aihui Zhou·Jun 26, 2024SaveLearn