Thermalization in the one-dimensional Salerno model lattice

Abstract

The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (non-integrable) discrete nonlinear Schr{ö}dinger (DNLS) one. The competition of local on-site nonlinearity and nonlinear dispersion governs the thermalization of this model. Here, we investigate the statistical mechanics of the Salerno one-dimensional lattice model in the nonintegrable case and illustrate the thermalization in the Gibbs regime. As the parameter interpolating between the two limits (from DNLS towards AL) is varied, the region in the space of initial energy and norm-densities leading to thermalization expands. The thermalization in the non-Gibbs regime heavily depends on the finite system size; we explore this feature via direct numerical computations for different parametric regimes.

11 figures

References in corpus (30)

• Discrete Breathers
• The Lyapunov Characteristic Exponents and their computation
• Finite thermal conductivity in 1d lattices
• Statistical mechanics of a nonlinear discrete system
• Localized States in Discrete Nonlinear Schrödinger Equations
• A route to thermalization in the $\alpha$-Fermi-Pasta-Ulam system
• Intermittent many-body dynamics at equilibrium
• The Fermi-Pasta-Ulam problem revisited: stochasticity thresholds in nonlinear Hamiltonian systems
• Delocalized Glassy Dynamics and Many Body Localization
• A simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities
• Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
• Negative Temperature States in the Discrete Nonlinear Schroedinger Equation
• The nonequilibrium discrete nonlinear Schroedinger equation
• Statistical mechanics of general discrete nonlinear Schr{ö}dinger models: Localization transition and its relevance for Klein-Gordon lattices
• KAM tori in 1D random discrete nonlinear Schrödinger model?
• Discrete Nonlinear Schr{ö}dinger Breathers in a Phonon Bath
• Ergodicity Breaking in a Deterministic Dynamical System
• Threshold for Chaos and Thermalization in One-Dimensional Mean-Field Bose-Hubbard Model
• Dynamical freezing of relaxation to equilibrium
• Dynamical Glass and Ergodization Times in Classical Josephson Junction Chains
• Discrete Solitons in the Salerno Model with competing nonlinearities
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• Dynamical glass in weakly non-integrable Klein-Gordon chains
• Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities
• Phase transitions at high energy vindicate negative microcanonical temperature
• Statistical Mechanics of a Discrete Schrödinger Equation with Saturable Nonlinearity
• Chaoticity without thermalisation in disordered lattices
• Quench dynamics in disordered two-dimensional Gross-Pitaevskii Lattices
• Nonlinearity and discreteness: Solitons in lattices
• Chaos and Thermalization in the one-dimensional Bose-Hubbard model in the classical-field approximation

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• How close Are Integrable and Non-integrable Models: A Parametric Case Study Based on the Salerno Model
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