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We develop a highly efficient method to numerically simulate thermalfluctuations and correlations in non-relativistic continuous bosonicone-dimensional systems. The method is suitable for arbitrary localinteractions as long as the system remains dynamically stable. We start byproving the equivalence of describing the systems through the transfer matrixformalism and a Fokker-Planck equation for a distribution evolving in space.The Fokker-Planck equation is known to be equivalent to a stochasticdifferential (It\={o}) equation. The latter is very suitable for computersimulations, allowing the calculation of any desired correlation function. Asan illustration, we apply our method to the case of two tunnel-coupledquasi-condensates of bosonic atoms. The results are compared to the predictionsof the sine-Gordon model for which we develop analytic expressions directlyfrom the transfer matrix formalism.

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