Thermalization of the Ablowitz-Ladik lattice in the presence of non-integrable perturbations

TL;DR

This paper explores how the integrable Ablowitz-Ladik lattice thermalizes under non-integrable perturbations, demonstrating that it reaches a Rayleigh-Jeans distribution characterized by temperature and chemical potential, with implications for optical thermodynamics.

Contribution

It shows that weakly nonlinear perturbations cause the Ablowitz-Ladik lattice to thermalize into a Rayleigh-Jeans distribution, highlighting the role of chaos and non-Hermitian effects in optical thermodynamics.

Findings

Thermalization into Rayleigh-Jeans distribution with temperature and chemical potential.

Chaos influences the thermalization process in the perturbed Ablowitz-Ladik system.

Non-local, non-Hermitian nonlinearity can facilitate thermalization in a periodic array.

Abstract

We investigate the statistical mechanics of the photonic Ablowitz-Ladik lattice, the integrable version of the discrete nonlinear Schr\"odinger equation. In this regard, we demonstrate that in the presence of perturbations the complex response of this system can be accurately captured within the framework of optical thermodynamics. Along these lines, we shed light on the true relevance of chaos in the thermalization of the Ablowitz-Ladik system. Our results indicate that when linear and nonlinear perturbations are incorporated, this weakly nonlinear lattice will thermalize into a proper Rayleigh-Jeans distribution with a well-defined temperature and chemical potential. This result illustrates that in the supermode basis, a non-local and non-Hermitian nonlinearity can in fact properly thermalize this periodic array in the presence of two quasi-conserved quantities