Thermalization in the one-dimensional Salerno model lattice

TL;DR

This paper studies how the one-dimensional Salerno lattice model thermalizes, focusing on the transition between integrable and non-integrable regimes and how initial conditions and system size influence thermalization.

Contribution

It provides a detailed analysis of thermalization behavior in the Salerno model, highlighting the impact of the interpolation parameter and finite system size.

Findings

Thermalization region expands as the model interpolates from DNLS to AL.

Thermalization depends heavily on system size in the non-Gibbs regime.

Numerical simulations confirm the influence of initial energy and norm-density on thermalization.

Abstract

The Salerno model constitutes an intriguing interpolation between the integrable Ablowitz-Ladik (AL) model and the more standard (non-integrable) discrete nonlinear Schr{\"o}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.