Dynamics of a 2D Bose-Einstein Condensate With an Impurity

Abstract

In this project we have studied the hydrodynamic forces that are acting on a small impurity submerged into a two-dimensional Bose-Einstein condensate at finite temperature. The condensate is modeled by the damped Gross-Pitaevskii equation which we have coupled to a repulsive Gaussian potential to model the interaction with the impurity. We have considered a weakly coupled impurity in an untrapped condensate. The perturbations away from the condensates ground-state, both the ones caused by the particle and those that are not, are assumed to be small. We therefore use linear perturbation analysis to find expressions for the hydrodynamic forces and compare these expressions to the classical Maxey-Riley equation. We find that the force caused by the perturbations that were in the fluid in the absence of the particle are proportional to the local condensate acceleration. This is analogous to the inertial term in the Maxey-Riley equation. The force due to the perturbations that were caused by the impurity takes, for slowly moving impurities in the steady-state, the form of the Stokes’ drag. The obtained expressions are then compared to numerical simulations.