Full counting statistics and large deviations in thermal 1D Bose gas

TL;DR

This paper derives the full counting statistics for the number of atoms in a 1D Bose gas modeled by Lieb-Liniger, revealing non-Gaussian fluctuations and enhanced large deviations in certain regimes.

Contribution

It provides the first detailed distribution of atom number fluctuations in the 1D interacting Bose gas across various temperatures and interval lengths.

Findings

Distribution deviates from Gaussian outside the quasi-condensate regime

Large number fluctuations are significantly enhanced for short intervals

Results are valid in the weakly interacting regime over a broad parameter window

Abstract

We obtain the distribution of number of atoms in an interval (full counting statistics) of Lieb-Liniger model of interacting bosons in one dimension. Our results are valid in the weakly interacting regime in a parametrically large window of temperatures and interval lengths. The obtained distribution deviates strongly from a Gaussian away from the quasi-condensate regime, and, for sufficiently short intervals, the probability of large number fluctuations is strongly enhanced.