Mean-Field Limits in Statistical DynamicsThese lectures notes are aimed at introducing the reader to some recent mathematical tools and results for the mean-field limit in statistical dynamics. As a warm-up, lecture 1 reviews the approach…François Golse·Jan 6, 2022SaveLearn
Symmetric Fermi projections and Kitaev's table: topological phases of matter in low dimensionsWe review Kitaev's celebrated "periodic table" for topological phases of condensed matter, which identifies ground states (Fermi projections) of gapped periodic quantum systems up to…David Gontier, Domenico Monaco, Solal Perrin-Roussel·Jan 5, 2022SaveLearn
A stochastic particle system approximating the BGK equationWe consider a stochastic N-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [2], we…Paolo Buttà, Mario Pulvirenti·Jan 5, 2022SaveLearn
Evolution of interface singularities in shallow water equations with variable bottom topographyWave front propagation with non-trivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of non-smooth initial data is examined, and in particular the…R. Camassa, R. D'Onofrio, G. Falqui et al.·Jan 5, 2022SaveLearn
Magnetic ring chains with vertex coupling of a preferred orientationWe discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex coupling is manifestly…Marzieh Baradaran, Pavel Exner, Jiri Lipovsky·Jan 5, 2022SaveLearn
On the equilibrium of the Poisson-Nernst-Planck-Bikermann model equipping with the steric and correlation effectsThe Poisson-Nernst-Planck-Bikermann (PNPB) model, in which the ions and water molecules are treated as different species with non-uniform sizes and valences with interstitial voids, can describe the…Jian-Guo Liu, Yijia Tang, Yu Zhao·Jan 5, 2022SaveLearn
Local Noether theorem for quantum lattice systems and topological invariants of gapped statesWe study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed (d+2)-form on the…Anton Kapustin, Nikita Sopenko·Jan 4, 2022SaveLearn
Will Random Cone-wise Linear Systems Be Stable?We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either v=Av or…Théo Dessertaine, Jean-Philippe Bouchaud·Jan 4, 2022SaveLearn
Spectrum of the transfer matrices of the spin chains associated with the A(2)3 Lie algebraWe study the exact solution of quantum integrable system associated with the A(2)3 twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the U(1) symmetry…Guang-Liang Li, Junpeng Cao, Xiao-Tian Xu et al.·Jan 4, 2022SaveLearn
Klein-Gordon equation in q-deformed Euclidean spaceWe introduce q-versions of the Klein-Gordon equation in the three-dimensional q-deformed Euclidean space. We determine plane wave solutions to our q-deformed Klein-Gordon equations. We show…Hartmut Wachter·Jan 4, 2022SaveLearn
Local minimality properties of circular motions in 1/rα potentials and of the figure-eight solution of the 3-body problemWe first take into account variational problems with periodic boundary conditions, and briefly recall some sufficient conditions for a periodic solution of the Euler-Lagrange equation to be either a…Marco Fenucci·Jan 4, 2022SaveLearn
Dirac Spinors on Generalised Frame Bundles: a frame bundle formulation for Einstein-Cartan-Dirac theoryWe clarify the structure obtained in Hélein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less…Jérémie Pierard de Maujouy·Jan 4, 2022SaveLearn
Darboux inversions of the Kepler problemWhile extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with the striking…Alain Albouy, Lei Zhao·Jan 3, 2022SaveLearn
Random vortex dynamics via functional stochastic differential equationsIn this paper we present a novel, closed three-dimensional (3D) random vortex dynamics system, which is equivalent to the Navier--Stokes equations for incompressible viscous fluid flows. The new…Zhongmin Qian, Endre Süli, Yihuang Zhang·Jan 3, 2022SaveLearn
Vortex pairs and dipoles on closed surfacesWe set up general equations of motion for point vortex systems on closed Riemannian surfaces, allowing for the case that the sum of vorticities is not zero and there hence must be counter-vorticity…Björn Gustafsson·Jan 3, 2022SaveLearn
Halliday-Suranyi Approach to the Anharmonic OscillatorIn this contribution to Peter Suranyi Festschrift, we study the Halliday-Suranyi perturbation method for calculating the energy eigenvalues of the quartic anharmonic oscillator.Nabin Bhatta, Tatsu Takeuchi·Jan 3, 2022SaveLearn
Rank 1 perturbations in random matrix theory -- a review of exact resultsA number of random matrix ensembles permitting exact determination of their eigenvalue and eigenvector statistics maintain this property under a rank 1 perturbation. Considered in this review are…Peter J. Forrester·Jan 2, 2022SaveLearn
Hamiltonian Dynamics of a spaceship in Alcubierre and Gödel metrics: Recursion operators and underlying master symmetriesWe study the Hamiltonian dynamics of a spaceship in the background of Alcubierre and Gödel metrics. We derive the Hamiltonian vector fields governing the system evolution, construct and discuss…Mahouton Norbert Hounkonnou, Mahougnon Justin Landalidji, Melanija Mitrovíc·Jan 2, 2022SaveLearn
On the Correlation Functions of the Characteristic Polynomials of Random Matrices with Independent Entries: Interpolation Between Complex and Real CasesThe paper is concerned with the correlation functions of the characteristic polynomials of random matrices with independent complex entries. We investigate how the asymptotic behavior of the…Ievgenii Afanasiev·Jan 1, 2022SaveLearn
Nonlinear Anderson localized states at arbitrary disorderIt is classical, following Furstenberg's theorem on positive Lyapunov exponent for products of random SL(2, R) matrices, that the one dimensional random Schrödinger operator has…Wencai Liu, W. -M. Wang·Jan 1, 2022SaveLearn
Nonlinear Classical and Quantum Integrable Systems with PT-symmetriesA key feature of integrable systems is that they can be solved to obtain exact analytical solutions. We show how new models can be constructed through generalisations of some well known nonlinear…Julia Cen·Jan 1, 2022SaveLearn
General Covariance from the Viewpoint of StacksGeneral covariance is a crucial notion in the study of field theories in curved spacetime. A field theory defined with respect to a semi-Riemannian metric is generally covariant if two metrics which…Filip Dul·Dec 31, 2021SaveLearn
Reduction of path integrals for interacting systems: The case of using dependent coordinates in the description of reduced motion on the orbit spaceWe consider a reduction procedure in Wiener-type path integral for a finite-dimensional mechanical system with a symmetry representing the motion of two interacting scalar particles on a manifold…S. N. Storchak·Dec 31, 2021SaveLearn
Hamiltonian Monodromy via spectral Lax pairsHamiltonian Monodromy is the simplest topological obstruction to the existence of global action-angle coordinates in a completely integrable system. We show that this property can be studied in a…G. J. Gutierrez Guillen, D. Sugny, P. Mardesic·Dec 31, 2021SaveLearn
Algebras of integrals of motion for the Hamilton-Jacobi and Klein-Gordon-Fock equations in spacetime with a four-parameter groups of motions in the presence of an external electromagnetic fieldThe algebras of the integrals of motion of the Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle moving in an external electromagnetic field in a spacetime manifold are…V. V. Obukhov·Dec 30, 2021SaveLearn