Thermalization of interacting quasi-one-dimensional systems

TL;DR

This paper develops a Boltzmann-equation approach to understand how weak interchain couplings thermalize quasi-one-dimensional systems, revealing a broad spectrum of relaxation times and non-exponential approach to equilibrium.

Contribution

It introduces an asymptotically exact collision integral formalism for integrable systems and applies it to coupled Bose gases, providing a quantitative theory of their relaxation dynamics.

Findings

Relaxation involves a broad spectrum of timescales.

The late-time Markov process is gapless.

Approach to equilibrium is non-exponential even for uniform perturbations.

Abstract

Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intra-chain interactions and the weak interchain coupling. When the intra-chain interactions are integrable, weak interchain couplings play a crucial part in thermalizing the system. Here, we develop a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and apply it to develop a quantitative theory of relaxation in coupled Bose gases in the experimentally relevant Newton's cradle setup. We find that relaxation involves a broad spectrum of timescales. We provide evidence that the Markov process governing relaxation at late times is gapless; thus, the approach to equilibrium is generally non-exponential, even for spatially uniform perturbations.