Non-perturbative method to compute thermal correlations in one-dimensional systems

TL;DR

This paper introduces a novel, efficient numerical method for simulating thermal fluctuations and correlations in one-dimensional bosonic systems, applicable to various local interactions and validated against analytical models.

Contribution

The authors develop a non-perturbative, stochastic differential equation-based approach to compute thermal correlations in 1D bosonic systems, bridging transfer matrix and Fokker-Planck formalisms.

Findings

Method accurately computes correlations in 1D bosonic systems.

Validated against sine-Gordon model predictions.

Applicable to arbitrary local interactions with stability.

Abstract

We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. The method is suitable for arbitrary local interactions as long as the system remains dynamically stable. We start by proving the equivalence of describing the systems through the transfer matrix formalism and a Fokker-Planck equation for a distribution evolving in space. The Fokker-Planck equation is known to be equivalent to a stochastic differential (It\={o}) equation. The latter is very suitable for computer simulations, allowing the calculation of any desired correlation function. As an illustration, we apply our method to the case of two tunnel-coupled quasi-condensates of bosonic atoms. The results are compared to the predictions of the sine-Gordon model for which we develop analytic expressions directly from the transfer matrix formalism.