Density Fluctuations in Uniform Quantum Gases

TL;DR

This paper provides analytical expressions for the static structure factor and pair correlation function in uniform ideal Bose-Einstein and Fermi-Dirac gases across all temperatures, revealing long-range correlations near BEC and quantum statistical effects.

Contribution

It introduces exact analytical formulas for g(r) and S(k) in quantum gases, highlighting their behavior near BEC and in dilute limits, with numerical results matching experimental observations.

Findings

g(r) becomes long-ranged near BEC temperature

Bosons exhibit bunching, fermions exhibit anti-bunching

Numerical values align with experimental data on density fluctuations

Abstract

Analytical expressions are given for the static structure factor S(k) and the pair correlation function g(r) for uniform ideal Bose-Einstein and Fermi-Dirac gases for all temperatures. In the vicinity of Bose Einstein condensation (BEC) temperature, g(r) becomes long ranged and remains so in the condensed phase. In the dilute gas limit, g(r) of bosons & fermions do not coincide with Maxwell-Boltzmann gas but exhibit bunching & anti-bunching effect respectively. The width of these functions depends on the temperature and is scaled as \surd (inverse atomic mass). Our numerical results provide the precise quantitative values of suppression/increase (antibunching and bunching) of the density fluctuations at small distances in ideal quantum gases in qualitative agreement with the experimental observation for almost non-trapped dilute gases.