Generalized Gibbs ensemble and work statistics of a quenched Luttinger liquid

TL;DR

This paper investigates the work distribution in a quenched Luttinger liquid, showing it can be described by a generalized Gibbs ensemble and analyzing how it varies with system size and quench parameters.

Contribution

It introduces a generalized Gibbs ensemble framework for describing work statistics in a quenched Luttinger liquid, including explicit intermode correlations.

Findings

Work PDF is non-Gaussian with a maximum around excess heat in the thermodynamic limit.

In small systems, the PDF shows a delta peak at adiabatic energy and oscillations with dips.

The study discusses implications for cold atom experiments.

Abstract

We analyze the probability distribution function (PDF) of work done on a Luttinger liquid for an arbitrary finite duration interaction quench and show that it can be described in terms a generalized Gibbs ensemble. We construct the corresponding density matrix with explicit intermode correlations, and determine the duration and interaction dependence of the probability of an adiabatic transition and the PDF of non-adiabatic processes. In the thermodynamic limit, the PDF of work exhibits a non-Gaussian maximum around the excess heat, carrying almost all spectral weight. In contrast, in the small system limit most spectral weight is carried by a delta peak at the energy of the adiabatic process, and an oscillating PDF with dips at energies commensurate to the quench duration and with an exponential envelope develops. Relevance to cold atom experiments is also discussed.