Classical fields approximation for cold weakly interacting bosons without free parameters

TL;DR

This paper improves the classical fields approximation for cold weakly interacting bosons by removing grid dependence through a new postulate linking the system's temperature to that of an ideal Bose gas, enabling a unified treatment of the entire system.

Contribution

It introduces a new postulate that eliminates the grid dependence in classical fields approximation, allowing for accurate modeling of the whole bosonic system at thermal equilibrium.

Findings

Nearly all atoms are within the classical fields with the new assumption.

The method becomes applicable to the entire system, both condensed and uncondensed parts.

Results are independent of the numerical grid used in simulations.

Abstract

Classical fields approximation to cold weakly interacting bosons allows for a unified treatment of condensed and uncondensed parts of the system. Until now, however, the quantitative predictions were limited by a dependence of the results on a grid chosen for numerical implementation of the method. In this paper we propose replacing this unphysical ambiguity by an additional postulate: the temperature of the gas at thermal equilibrium should be the same as that of an ideal Bose gas with the same fraction of condensed atoms. As it turns-out, with this additional assumption, nearly all atoms are within the classical fields, thus the method applies to the whole system.