Non-equilibrium Dynamics of Vortices in Two-Dimensional Quantum Gases: Determining the Dynamical Scaling Region Using the Mahalanobis Distance

Abstract

AbstractWhen a system undergoes a rapid quench from a disordered to an ordered phase, it does not order instantly but instead relaxes towards equilibrium over time. During this relaxation, the dynamical scaling hypothesis predicts that the length scale of ordered regions increases, with later patterns statistically similar to earlier ones except for a change in global scale. Quantum gases are one of many systems in which such out of equilibrium behaviour is predicted to occur. Here, we present a method for systematically testing when dynamical scaling is taking place, by quantifying the similarity of the rescaled two-point correlation function over time using the Mahalanobis distance. Data on the velocity field of a two-dimensional quantum fluid, generated from point vortex simulations, are used to illustrate the application of this method.