Expectation Values in the Lieb-Liniger Bose Gas

TL;DR

This paper introduces a new method leveraging an exact mapping to efficiently compute expectation values in the Lieb-Liniger Bose gas at various temperatures, including the three-body expectation value relevant for recombination rates.

Contribution

It presents a novel approach based on an exact mapping to calculate expectation values in the Lieb-Liniger model at finite temperature, with improved convergence properties.

Findings

Efficient computation of expectation values at finite temperature.

Series with remarkable convergence behavior.

Calculation of three-body expectation value relevant for recombination.

Abstract

Taking advantage of an exact mapping between a relativistic integrable model and the Lieb-Liniger model we present a novel method to compute expectation values in the Lieb-Liniger Bose gas both at zero and finite temperature. These quantities, relevant in the physics of one-dimensional ultracold Bose gases, are expressed by a series that has a remarkable behavior of convergence. Among other results, we show the computation of the three-body expectation value at finite temperature, a quantity that rules the recombination rate of the Bose gas.