Statistics of the work done by splitting a one-dimensional quasi-condensate

TL;DR

This paper investigates the statistical properties of work done during a quantum quench in a one-dimensional bosonic system, revealing universal features and edge singularities linked to the critical Casimir effect.

Contribution

It provides a detailed analysis of work statistics in a 1D quasi-condensate, highlighting universal edge singularities and establishing a connection to the critical Casimir effect.

Findings

Edge singularity in work distribution at low energy threshold

Universal features as post-quench gap approaches zero

Exact results for non-interacting bosonic systems

Abstract

Motivated by experiments on splitting one-dimensional quasi-condensates, we study the statistics of the work done by a quantum quench in a bosonic system. We discuss the general features of the probability distribution of the work and focus on its behaviour at the lowest energy threshold, which develops an edge singularity. A formal connection between this probability distribution and the critical Casimir effect in thin classical films shows that certain features of the edge singularity are universal as the post-quench gap tends to zero. Our results are quantitatively illustrated by an exact calculation for non-interacting bosonic systems. The effects of finite system size, dimensionality, and non-zero initial temperature are discussed in detail.