Mapping of Coulomb gases and sine-Gordon models to statistics of random surfaces

TL;DR

This paper introduces a novel non-perturbative method to analyze a new class of sine-Gordon models by mapping them to the statistics of random surfaces, with applications to interference in low-dimensional Bose gases.

Contribution

The authors develop a new approach for calculating partition functions of sine-Gordon models with region-specific interactions, linking them to random surface statistics.

Findings

Derived full distribution functions of interference amplitudes for 1D and 2D Bose gases.

Applied the method to compute interference fringe amplitudes at nonzero temperatures.

Established a connection between sine-Gordon models and random surface statistics.

Abstract

We introduce a new class of sine-Gordon models, for which interaction term is present in a region different from the domain over which quadratic part is defined. We develop a novel non-perturbative approach for calculating partition functions of such models, which relies on mapping them to statistical properties of random surfaces. As a specific application of our method, we consider the problem of calculating the amplitude of interference fringes in experiments with two independent low dimensional Bose gases. We calculate full distribution functions of interference amplitude for 1D and 2D gases with nonzero temperatures.