Non-perturbative method to compute thermal correlations in one-dimensional systems: A brief overview

TL;DR

This paper introduces a non-perturbative, efficient numerical method for calculating thermal correlations in one-dimensional bosonic systems, leveraging a stochastic differential equation approach for accurate simulations.

Contribution

The authors develop a novel computational technique connecting transfer matrix formalism with stochastic equations to simulate thermal fluctuations in 1D bosonic systems.

Findings

Successfully applied to tunnel-coupled quasicondensates.

Enables calculation of arbitrary correlation functions.

Provides a highly efficient simulation framework.

Abstract

We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. We start by noticing the equivalence of their description through the transfer matrix formalism and a Fokker-Planck equation for a distribution evolving in space. The corresponding stochastic differential (It\={o}) equation is very suitable for computer simulations, allowing the calculation of arbitrary correlation functions. As an illustration, we apply our method to the case of two tunnel-coupled quasicondensates of bosonic atoms.