Caustics in the sine-Gordon model from quenches in coupled 1D Bose gases

TL;DR

This paper investigates the emergence of caustics in the non-equilibrium dynamics of coupled 1D Bose gases using the sine-Gordon model, revealing characteristic probability distributions influenced by thermal noise.

Contribution

It demonstrates how caustics form and evolve in a non-equilibrium quantum field theory setting, specifically in coupled ultracold Bose gases, incorporating thermal effects.

Findings

Caustics dominate the dynamics after quenching the gases.

Probability distributions develop a 'circus tent' shape over time.

Thermal noise influences the formation and evolution of caustics.

Abstract

Caustics are singularities that occur naturally in optical, hydrodynamic and quantum waves, giving rise to high amplitude patterns that can be described using catastrophe theory. In this paper we study caustics in a statistical field theory setting in the form of the sine-Gordon model that describes a variety of physical systems including coupled 1D superfluids. Specifically, we use classical field simulations to study the dynamics of two ultracold 1D Bose gases (quasi-condensates) that are suddenly coupled to each other and find that the resulting non-equilibrium dynamics are dominated by caustics. Thermal noise is included by sampling the initial states from a Boltzmann distribution for phononic excitations. We find that caustics pile up over time in both the number and phase difference observables leading to a characteristic non-thermal `circus tent' shaped probability distribution at long times.