Exact three-body local correlations for excited states of the 1D Bose gas

TL;DR

This paper provides an exact analytic formula for three-body local correlations in the 1D Bose gas, applicable to thermal and certain excited states, with implications for understanding thermalization and particle loss.

Contribution

It introduces a novel exact expression for three-body correlations in the Lieb-Liniger model, extending analysis to non-thermal excited states and finite temperature scenarios.

Findings

Exact formula for three-body correlations derived

Results applicable to thermal and non-thermal states

Finite temperature and confinement effects analyzed

Abstract

We derive an exact analytic expression for the three-body local correlations in the Lieb-Liniger model of 1D Bose gas with contact repulsion. The local three-body correlations control the thermalization and particle loss rates in the presence of terms which break integrability, as is realized in the case of 1D ultracold bosons. Our result is valid not only at finite temperature but also for a large class of non-thermal excited states in the thermodynamic limit. We present finite temperature calculations in the presence of external harmonic confinement within local density approximation, and for a highly excited state that resembles an experimentally realized configuration.