Exact Results for Three-Body Correlations in a Degenerate One-Dimensional Bose Gas

TL;DR

This paper derives an exact formula for three-body correlations in a one-dimensional Bose gas, valid across all interaction strengths, and explores finite-size effects in small systems.

Contribution

It provides a novel exact expression for the three-body correlation function in the Lieb-Liniger model, unifying previous regimes and including finite-size analysis.

Findings

Exact correlation function expressed in terms of thermodynamic parameters

Valid for all interaction regimes, including Bogoliubov and Tonks-Girardeau limits

Finite-size effects characterized for small particle systems

Abstract

Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic parameters of the Lieb-Liniger model, is valid for all values of the dimensionless coupling $\gamma$ and contains the previously known results for the Bogoliubov and Tonks-Girardeau regimes as limiting cases. We also investigate finite-size effects by calculating the correlation function for small systems of 3, 4, 5 and 6 particles.