Metropolis-Hastings thermal state sampling for numerical simulations of Bose-Einstein condensates

TL;DR

This paper applies the Metropolis-Hastings algorithm to efficiently sample thermal states of one-dimensional Bose-Einstein quasicondensates, including generalized Gibbs ensembles, aiding thermodynamic studies of integrable systems.

Contribution

It introduces a versatile Metropolis-Hastings sampling method for Bose-Einstein condensates that can handle various trap geometries and ensembles, including generalized Gibbs.

Findings

Successfully samples thermal states in untrapped and trapped cases

Can incorporate quantum noise in simulations

Extends to generalized Gibbs ensemble sampling

Abstract

We demonstrate the application of the Metropolis-Hastings algorithm to sampling of classical thermal states of one-dimensional Bose-Einstein quasicondensates in the classical fields approximation, both in untrapped and harmonically trapped case. The presented algorithm can be easily generalized to higher dimensions and arbitrary trap geometry. For truncated Wigner simulations the quantum noise can be added with conventional methods (half a quantum of energy in every mode). The advantage of the presented method over the usual analytical and stochastic ones lies in its ability to sample not only from canonical and grand canonical distributions, but also from the generalized Gibbs ensemble, which can help to shed new light on thermodynamics of integrable systems.