A simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities

Abstract

The localization of energy in the discrete nonlinear Schroedinger equation is explained with statistical methods. The partition function and the entropy of the system are computed for low-amplitude initial conditions. Detailed predictions for the long-time solution are derived.

References in corpus (6)

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• Statistical mechanics of a nonlinear discrete system
• Growth and decay of discrete nonlinear Schroedinger breathers interacting with internal modes or standing-wave phonons
• Standing wave instabilities in a chain of nonlinear coupled oscillators
• Localization and Coherence in Nonintegrable Systems
• Decay of DNLS breathers through inelastic multiphonon scattering

Cited by in corpus (43)

• Asymptotic quantum many-body localization from thermal disorder
• Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
• Negative Temperature States in the Discrete Nonlinear Schroedinger Equation
• Statistical mechanics of general discrete nonlinear Schr{ö}dinger models: Localization transition and its relevance for Klein-Gordon lattices
• The nonequilibrium discrete nonlinear Schroedinger equation
• Statistical Mechanics of Systems with Negative Temperature
• Dynamical freezing of relaxation to equilibrium
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• Off-equilibrium Langevin dynamics of the discrete nonlinear Schroedinger chain
• Discrete breathers in thermal equilibrium: distributions and energy gaps
• Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos
• Condensation transition in joint large deviations of linear statistics
• A Chain, a Bath, a Sink and a Wall
• Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation
• Phase transitions at high energy vindicate negative microcanonical temperature
• Chaos and localization in the Discrete Nonlinear Schrödinger Equation
• Thermalization of Strongly Disordered Nonlinear Chains
• Entropic thermodynamics of nonlinear photonic chain networks
• Relaxation and coarsening of weakly-interacting breathers in a simplified DNLS chain
• Effective mobility and diffusivity in coarsening processes
• Non-Gibbs states on a Bose-Hubbard lattice
• Statistical Mechanics of a Discrete Schrödinger Equation with Saturable Nonlinearity
• Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
• Negative temperature states as exact equilibrium solutions of the Wave Kinetic equation for one dimensional lattices
• Density Resolved Wave Packet Spreading in Disordered Gross-Pitaevskii Lattices
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Localization in the Discrete Non-Linear Schrödinger Equation and geometric properties of the microcanonical surface
• Thermalized polarization dynamics of a discrete optical waveguide system with four-wave mixing
• Coupled transport in a linear-stochastic Schrödinger Equation
• Thermalization in the one-dimensional Salerno model lattice
• Exact solutions for a coherent phenomenon of condensation in conservative Hamiltonian systems
• Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian
• Glassy dynamics in strongly anharmonic chains of oscillators
• Quench dynamics in disordered two-dimensional Gross-Pitaevskii Lattices
• Mechanisms for transient localization in a diatomic nonlinear chain
• Probabilistic methods for discrete nonlinear Schrödinger equations
• Thermalization in a nonlinear variant of the discrete nonlinear Schrödinger Equation
• Transient ordering in the Gross-Pitaevskii lattice subject to an energy quench within the disordered phase
• Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers
• Localization and "classical entanglement'' in the Discrete Non-Linear Schrödinger Equation
• Solitons and Gibbs measures for nonlinear Schroedinger equations
• Infinite-temperature thermostats by energy localization in a nonequilibrium setup
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization