Prethermalization in coupled one-dimensional quantum gases

TL;DR

This paper investigates how coupled one-dimensional Bose gases reach non-thermal steady states, revealing a prethermalization plateau governed by quasi-conserved quantities, using a Boltzmann collision integral approach.

Contribution

It introduces a Boltzmann-based framework to analyze prethermalization in coupled 1D Bose gases and characterizes the non-thermal fixed point and associated generalized Gibbs ensemble.

Findings

Identification of a prethermalization plateau in coupled 1D Bose gases

Characterization of quasi-conserved quantities controlling the plateau

Construction of the generalized Gibbs ensemble for the non-thermal fixed point

Abstract

We consider the problem of the development of steady states in one-dimensional Bose gas tubes that are weakly coupled to one another through a density-density interaction. We analyze this development through a Boltzmann collision integral approach. We argue that when the leading order of the collision integral, where single particle-hole excitations are created in individual gases, is dominant, the state of the gas evolves first to a non-thermal fixed point, i.e. a prethermalization plateau. This order is dominant when a pair of tubes are inequivalent with, say, different temperatures or different effective interaction parameters, $\gamma$. We characterize this non-thermal prethermalization plateau, constructing both the quasi-conserved quantities that control the existence of this plateau as well as the associated generalized Gibbs ensemble.