Classical field records of a quantum system: their internal consistency and accuracy

TL;DR

This paper assesses the accuracy of classical field descriptions for quantum Bose gases across different dimensions, identifying regimes where they are reliable and explaining discrepancies in previous results.

Contribution

It provides a detailed analysis of the validity regimes for classical field methods in quantum Bose gases, including the impact of energy cutoffs and observable dependencies.

Findings

Classical field methods are accurate below specific temperature thresholds in 1d and 3d.

In 2d, classical fields cannot simultaneously match key quantum observables at zero temperature.

The optimal energy cutoff varies significantly depending on the observable considered.

Abstract

We determine the regime where the widespread classical field description for quantum Bose gases is quantitatively accurate in 1d, 2d, and 3d by a careful study of the ideal gas limit. Numerical benchmarking in 1d shows that the ideal gas results carry over unchanged into the weakly interacting gas. The optimum high energy cutoff is in general shown to depend strongly on the observable in question (e.g. energy, density fluctuations, phase coherence length, condensate fraction). This explains the wide spread of past results. A consistent classical field representation with less than 10% deviation in all typical observables can be given for systems at temperatures below 0.0064 degeneracy temperature in 1d, and 0.49 critical temperature in 3d. Surprisingly, this is not possible for the 2d ideal gas even at zero temperature because mean density, density fluctuations and energy cannot be simultaneously matched to the quantum results.