Dynamics of Uniform Quantum Gases, I: Density and Current Correlations

TL;DR

This paper develops a comprehensive analytical framework for density and current response functions in uniform ideal quantum gases across all conditions, revealing long-range correlations in Bose condensates and short-range in others.

Contribution

It provides exact analytical expressions for spectral functions and susceptibilities, and explores the effects of interactions and temperature on correlation ranges and superfluidity.

Findings

Long-range current correlations in Bose-condensed gases.

Short-range correlations in Fermi and non-condensed bosons.

Analytical expressions involving polylogarithms and Kummer functions.

Abstract

A unified approach valid for any wavenumber, frequency, and temperature is presented for uniform ideal quantum gases allowing for a comprehensive study of number density and particle-current density response functions. Exact analytical expressions are obtained for spectral functions in terms of polylogarithms. Also, particle-number and particle-current static susceptibilities are presented which, for fugacity less than unity, additionally involve Kummer functions. The wavenumber and temperature dependent transverse-current static susceptibility is used to show explicitly that current correlations are of a long range in a Bose-condensed uniform ideal gas but for bosons above the critical temperature and for Fermi and Boltzmann gases at all temperatures these correlations are of short range. Contact repulsive interactions for systems of neutral quantum particles are considered within the random-phase approximation. The expressions for particle-number and transverse-current susceptibilities are utilized to discuss the existence or nonexistence of superfluidity in the systems under consideration.