Caustics in the sine-Gordon model from quenches in coupled one-dimensional Bose gases

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 one-dimensional (1D) superfluids. Specifically, we use classical field simulations to study the dynamics of two ultracold 1D Bose gases (quasicondensates) that are suddenly coupled to each other and find that the resulting nonequilibrium dynamics is 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 nonthermal circus-tent-shaped probability distribution at long times.