Quantum versus classical statistical dynamics of an ultracold Bose gas

TL;DR

This paper compares quantum and classical statistical dynamics in ultracold Bose gases, identifying when quantum fluctuations significantly influence experimental outcomes using advanced functional-integral techniques.

Contribution

It introduces a nonperturbative 2PI 1/N expansion approach to distinguish quantum from classical dynamics in ultracold Bose gases, establishing a 'classicality' condition.

Findings

Quantum fluctuations become relevant under specific conditions.

The 2PI 1/N expansion captures nonperturbative effects.

Distinctive properties of quantum versus classical dynamics are identified.

Abstract

We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and Hartree-Fock-Bogoliubov mean-field theories, which can be obtained as classical (statistical) field-theory approximations of the quantum many-body problem. We employ functional-integral techniques based on the two-particle irreducible (2PI) effective action. The role of quantum fluctuations is studied within the nonperturbative 2PI 1/N expansion to next-to-leading order. At this accuracy level memory-integrals enter the dynamic equations, which differ for quantum and classical statistical descriptions. This can be used to obtain a 'classicality' condition for the many-body dynamics. We exemplify this condition by studying the nonequilibrium evolution of a 1D Bose gas of sodium atoms, and discuss some distinctive properties of quantum versus classical statistical dynamics.