Exact large-scale fluctuations of the phase field in the sine-Gordon model

TL;DR

This paper develops an exact analytical framework for understanding large-scale phase fluctuations in the sine-Gordon model, integrating Ballistic Fluctuation Theory with Generalized Hydrodynamics, and confirms predictions with numerical simulations.

Contribution

It introduces the first exact theory for phase fluctuations in the sine-Gordon model applicable across all regimes, combining advanced theoretical methods.

Findings

Exact formulas for phase fluctuations at all regimes

Ballistic propagation of quasi-particles instead of diffusion

Numerical validation using Monte Carlo simulations

Abstract

We present the first exact theory and analytical formulas for the large-scale phase fluctuations in the sine-Gordon model, valid in all regimes of the field theory, for arbitrary temperatures and interaction strengths. Our result is based on the Ballistic Fluctuation Theory combined with Generalized Hydrodynamics, and can be seen as an exact ``dressing" of the phenomenological soliton-gas picture first introduced by Sachdev and Young [S. Sachdev and A. P. Young, PRL 78, 2220 (1997)], to the modes of Generalised Hydrodynamics. The resulting physics of phase fluctuations in the sine-Gordon model is qualitatively different, as the stable quasi-particles of integrability give coherent ballistic propagation instead of diffusive spreading. We provide extensive numerical checks of our analytical predictions within the classical regime of the field theory by using Monte Carlo methods. We discuss how our results are of ready applicability to experiments on tunnel-coupled quasicondensates.