Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases

TL;DR

This paper computes finite-temperature correlation functions in one-dimensional trapped and untrapped Bose gases, revealing universal scaling behaviors influenced by interaction strength and confinement.

Contribution

It provides a universal expression for correlation decay exponents valid across weak and strong interactions, incorporating trap effects and conjecturing density correlations.

Findings

Universal scaling exponent expression for correlations

Dependence of exponents on interaction strength and trap

Conjectured form for density-density correlations

Abstract

We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.