Application of Black-Hole Physics to Vortex Dynamics in Superfluids

Abstract

This thesis is concerned with the investigation of non-equilibrium dynamics and turbulence in two- and three-dimensional superfluids using an intrinsically non-perturbative holographic description in terms of field theories in higher-dimensional black-hole-anti-de Sitter spacetimes. We perform numerical real-time simulations of these systems on large numerical domains. In a first part, we study the kinematics of vortex dipoles in two dimensions. To this end, we introduce a high-precision track- ing routine to locate their cores. By matching to the vortex trajectories solutions of the dissipative Gross–Pitaevskii equation and of equations for the motion of point vortices, we quantify the strong dissipation of the superfluid, which in holography is related to the absorption of modes by the black hole. We conjecture holography to be applicable to vortex dynamics in films of superfluid helium and in oblate cold quantum gases. In a second part, we study for the first time vortex lines and rings in the three-dimensional holographic superfluid. We investigate their dynamics, and interactions, including the famous leapfrogging motion and scattering events of rings, as well as Kelvin-wave excitations of their cores. Further, we study the evolution of the superfluid starting from far-from-equilibrium initial conditions characterised by dense vortex tangles. We analyse the dynamics in terms of scaling behaviour in correlation functions and observe signatures of universal turbulent behaviour during different regimes of the evolution. This work constitutes the first ab initio study of the mentioned phenomena in a strongly dissipative three-dimensional superfluid.