Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion

TL;DR

This paper investigates how weak chaos and Arnold diffusion in a disordered nonlinear Schroedinger chain lead to the destruction of Anderson localization, resulting in long-term thermalization through chaotic spot migration.

Contribution

It introduces a novel spatial structure of chaos as a dilute gas of chaotic spots driving Arnold diffusion and derives macroscopic transport equations for this process.

Findings

Chaotic spots act as stochastic pumps causing local relaxation.

Migration of chaotic spots enables long-range thermalization.

Transport equations describe the macroscopic dynamics of the system.

Abstract

The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is argued that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of relaxation at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The cor- resonding macroscopic transport equations are obtained.