Stochastic field equation for the canonical ensemble of a Bose gas

TL;DR

This paper introduces a stable stochastic equation for simulating Bose gases in the canonical ensemble, effectively handling high-energy fluctuations and enabling detailed analysis of ground state and correlation properties across temperature regimes.

Contribution

The authors develop a novel norm-preserving stochastic evolution equation for Bose fields, improving numerical stability and applicability for non-interacting and weakly interacting Bose gases.

Findings

Stable simulation of Bose gases in various traps

Accurate ground state occupation number calculations

Effective suppression of high-energy fluctuations

Abstract

We present a novel norm preserving stochastic evolution equation for a Bose field. Ensemble averages are quantum expectation values in the canonical ensemble. This numerically very stable equation suppresses high-energy fluctuations exponentially, preventing cutoff problems to occur. We present 3D simulations for an ideal gas in various trapping potentials focussing on ground state occupation numbers and spatial correlation functions for a wide range of temperatures above and below the critical temperature. Although rigorously valid for non-interacting Bosons only, we argue that weakly interacting Bose gases may also be amenable to this approach, in the usual mean-field approximation.