# Quench action and large deviations: work statistics in the one-dimensional Bose gas

## TL;DR

This paper analyzes the large deviations of work in a one-dimensional Bose gas after an interaction quench, revealing non-Gaussian fluctuations near the mean and algebraic decay for larger deviations, using the quench action and Bethe ansatz.

## Contribution

It provides an exact computation of the rate function for work fluctuations in an interacting Bose gas post-quench, extending large deviation analysis to quantum integrable systems.

## Key findings

- Fluctuations near the mean are non-Gaussian.
- Large deviations below the mean are exponentially suppressed.
- Deviations above the mean decay algebraically with an unknown exponent.

## Abstract

We study the statistics of large deviations of the intensive work done in an interaction quench of a one-dimensional Bose gas with a large number N of particles, system size L and fixed density. We consider the case in which the system is initially prepared in the non-interacting ground state and a repulsive interaction is suddenly turned on. For large deviations of the work below its mean value, we show that the large deviation principle holds by means of the quench action approach. Using the latter, we compute exactly the so-called rate function, and study its properties analytically. In particular, we find that fluctuations close to the mean value of the work exhibit a marked non- Gaussian behavior, even though their probability is always exponentially suppressed below it as L increases. Deviations larger than the mean value, instead, exhibit an algebraic decay, whose exponent can not be determined directly by large-deviation theory. Exploiting the exact Bethe ansatz representation of the eigenstates of the Hamiltonian, we calculate this exponent for vanishing particle density. Our approach can be straightforwardly generalized to quantum quenches in other interacting integrable systems.