Classical fields in the one-dimensional Bose gas: applicability and determination of the optimal cutoff

TL;DR

This paper evaluates the classical field approach for the one-dimensional Bose gas at low temperatures, identifying optimal parameters and basis choices for accurate physical descriptions across different regimes.

Contribution

It provides a comprehensive analysis of the classical field method's accuracy, determines the optimal cutoff for various regimes, and compares basis choices for describing cold quantum gases.

Findings

Optimal cutoff increases with density and chemical potential.

Trap basis is better for low-temperature quantum regimes.

Estimates for key physical quantities are provided.

Abstract

To finalize information about the accuracy of the classical field approach for the 1d Bose gas, the lowest temperature quasicondensate was studied by comparing the extended Bogoliubov model of Mora and Castin, to its classical field analogue. The parameters for which the physics is well described by matter waves are now presented for all 1d regimes, and concurrently, the optimal cutoff that best matches all observables together is also provided. This cutoff rises strongly with density when the chemical potential is higher than the thermal energy to account for kinetic energy. As a consequence, clouds that reach this coldest quantum fluctuating regime are better described using a trap basis than plane waves. This contrasts with higher temperature clouds for which the basis choice is less important. In passing, estimates for chemical potential, density fluctuations, kinetic and interaction energy in the low temperature quasicondensate are obtained up to several leading terms.