Integrability of 4 Matrix Model as N-body Harmonic Oscillator SystemWe study a Hermitian matrix model with a kinetic term given by Tr (H 2 ), where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential…Harald Grosse, Akifumi Sako·Aug 22, 2023SaveLearn
Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii EquationWe consider the evolution of a gas of N bosons in the three-dimensional Gross-Pitaevskii regime (in which particles are initially trapped in a volume of order one and interact through a repulsive…Cristina Caraci, Jakob Oldenburg, Benjamin Schlein·Aug 22, 2023SaveLearn
Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinatesCurvilinear coordinate systems distinct from the rectangular Cartesian coordinate system are particularly valuable in the field calculations as they facilitate the expression of boundary conditions…Pavel Strunz·Aug 22, 2023SaveLearn
Response functions of many-body condensed matter systemsWe discuss rigorous results about the response functions of gapped and gapless interacting fermionic lattice models, relevant for the study of transport in condensed matter physics.Marcello Porta, Vieri Mastropietro, Alessandro Giuliani·Aug 22, 2023SaveLearn
Long persistence of localization in a disordered anharmonic chain beyond the atomic limitWe establish rigorous bounds on the decorrelation time and thermal transport in the disordered Klein-Gordon chain with a quartic on-site potential, governed by a parameter λ. At $λ =…Wojciech De Roeck, François Huveneers, Oskar A. Prośniak·Aug 22, 2023SaveLearn
Photon topologyThe topology of photons in vacuum is interesting because there are no photons with k=0, creating a hole in momentum space. We show that while the set of all photons forms a trivial…Eric Palmerduca, Hong Qin·Aug 22, 2023SaveLearn
Quantum Optimal Transport: Quantum Couplings and Many-Body ProblemsThis text is a set of lecture notes for a 4.5-hour course given at the Erd\"os Center (R\'enyi Institute, Budapest) during the Summer School "Optimal Transport on Quantum Structures" (September…François Golse·Aug 22, 2023SaveLearn
Chiral limit of twisted trilayer grapheneWe initiate the mathematical study of the Bistritzer-MacDonald Hamiltonian for twisted trilayer graphene in the chiral limit (and beyond). We develop a spectral theoretic approach to investigate the…Simon Becker, Tristan Humbert, Jens Wittsten et al.·Aug 21, 2023SaveLearn
Jacobi Group Symmetry of Hamilton's MechanicsWe show that the diffeomorphisms of an extended phase space with time, energy, momentum and position degrees of freedom that leave invariant the symplectic 2-form and and a degenerate orthogonal…Stephen G. Low, Rutwig Campoamor-Stursberg·Aug 21, 2023SaveLearn
Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn-Banach Theorem: II. PropertiesIn a companion article it was shown in a certain precise sense that, for any thermodynamical theory that respects the Kelvin-Planck Second Law, the Hahn-Banach Theorem immediately ensures the…Martin Feinberg, Richard B. Lavine·Aug 21, 2023SaveLearn
Heun-type solutions for the Dirac particle on the curved background of Minkowski space-timesIn the present paper, we study the Dirac equation in the background of Minkowski space-time on a light cone. With the help of the coupling of the radial parts, the system of 4 equations is reduced to…Saman Rahmani, Hossein Panahi, Amerne Najafizade·Aug 21, 2023SaveLearn
Modeling of electronic dynamics in twisted bilayer grapheneWe consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic…Tianyu Kong, Diyi Liu, Mitchell Luskin et al.·Aug 21, 2023SaveLearn
Boltzmann weights and fusion procedure for the rational seven-vertex SOS modelWe consider seven-vertex two-dimensional integrable statistical model. With the help of intertwining vector method we construct its counterpart integrable model of SOS type. More general models of…Pavel V. Antonenko, Pavel A. Valinevich·Aug 20, 2023SaveLearn
Microscopic derivation of a Schr\"odinger equation in dimension one with a nonlinear point interactionWe derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity…Riccardo Adami, Jinyeop Lee·Aug 18, 2023SaveLearn
Asymptotic Analysis for the Eigenvalues of Peridynamic OperatorsExplicit representations of the eigenvalues of the peridynamic operator have been recently derived in [5]. These representations are given in terms of generalized hypergeometric functions. Asymptotic…Bacim Alali, Nathan Albin, Thinh Dang·Aug 18, 2023SaveLearn
Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn-Banach Theorem: I. ExistenceThe Kelvin-Planck statement of the Second Law of Thermodynamics is a stricture on the nature of heat receipt by any body suffering a cyclic process. It makes no mention of temperature or of entropy.…Martin Feinberg, Richard B. Lavine·Aug 16, 2023SaveLearn
Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chainThis paper originates from lectures delivered at the summer school "Fundamental Problems in Statistical Physics XV" in Bruneck, Italy, in 2021. We give a brief and limited introduction into…Wojciech De Roeck, François Huveneers, Branko Meeus et al.·Aug 16, 2023SaveLearn
On the probability distributions of the force and potential energy for a system with an infinite number of random point sourcesIn this work, we study the probability distribution for the force and potential energy of a test particle interacting with N point random sources in the limit N→∞. The interaction…E. L. S. Silva, L. H. Miranda-Filho, A. Figueiredo·Aug 16, 2023SaveLearn
Synge's dynamic problem for two isolated point charges. A new method to find global solutions for Functional Differential Equations SystemSynge's problem consists in to determine the dynamics of two point electrical charges interacting through their electromagnetic fields, without to take into account the radiation terms due to the…Rodrigo R. Silva, Annibal Figueiredo·Aug 16, 2023SaveLearn
Semiclassical approach to the nonlocal nonlinear Schr\"odinger equation with a non-Hermitian termThe nonlinear Sch\"odinger equation (NLSE) with a non-Hermitian term is the model for various phenomena in nonlinear open quantum systems. We deal with the Cauchy problem for the nonlocal…A. E. Kulagin, A. V. Shapovalov·Aug 16, 2023SaveLearn
Boundary states of a bulk gapped ground state in 2-d quantum spin systemsWe introduce a natural mathematical definition of boundary states of a bulk gapped ground state, in the operator algebraic framework of 2-d quantum spin systems. With approximate Haag duality at…Yoshiko Ogata·Aug 16, 2023SaveLearn
Quantum Spin SystemsThis work provides an overview of gapped quantum spin systems, including concepts, techniques, properties, and results. The basic framework and objects of interest for quantum spin systems are…Amanda Young·Aug 15, 2023SaveLearn
Combinatorial QFT on graphs: first quantization formalismWe study a combinatorial model of the quantum scalar field with polynomial potential on a graph. In the first quantization formalism, the value of a Feynman graph is given by a sum over maps from the…Ivan Contreras, Santosh Kandel, Pavel Mnev et al.·Aug 15, 2023SaveLearn
Baxter operators in Ruijsenaars hyperbolic system IV. Coupling constant reflection symmetryWe introduce and study a new family of commuting Baxter operators in the Ruijsenaars hyperbolic system, different from that considered by us earlier. Using a degeneration of Rains integral identity…N. Belousov, S. Derkachov, S. Kharchev et al.·Aug 15, 2023SaveLearn
Polynomial Stochastic Dynamical IndicatorsThis paper introduces three types of dynamical indicators that capture the effect of uncertainty on the time evolution of dynamical systems. Two indicators are derived from the definition of Finite…Massimiliano Vasile, Matteo Manzi·Aug 15, 2023SaveLearn