Anisotropic scattering of Bogoliubov excitations

Universität Bayreuth - 95440 Bayreuth, Germany, EU

Corresponding author: christopher.gaul@uni-bayreuth.de

Received: 26 March 2008
Accepted: 22 May 2008

Abstract

We consider elementary excitations of an interacting Bose-Einstein condensate in the mean-field framework. As a building block for understanding the dynamics of systems comprising interaction and disorder, we study the scattering of Bogoliubov excitations by a single external impurity potential. A numerical integration of the Gross-Pitaevskii equation shows that the single-scattering amplitude has a marked angular anisotropy. By a saddle point expansion of the hydrodynamic mean-field energy functional, we derive the relevant scattering amplitude including the crossover from sound-like to particle-like excitations. The very different scattering properties of these limiting cases are smoothly connected by an angular envelope function with a well-defined node of vanishing scattering amplitude. We find that the overall scattering is most efficient at the crossover from phonon-like to particle-like Bogoliubov excitations.