Anisotropic scattering of Bogoliubov excitations

TL;DR

This paper investigates how Bogoliubov excitations in a Bose-Einstein condensate scatter anisotropically off impurities, revealing a smooth transition in scattering behavior from phonon-like to particle-like excitations.

Contribution

It introduces a detailed analysis of anisotropic scattering of Bogoliubov excitations, including a new analytical expression capturing the crossover from sound-like to particle-like behavior.

Findings

Scattering amplitude exhibits marked angular anisotropy.

Smooth crossover in scattering properties from phonon-like to particle-like excitations.

Maximum scattering occurs at the crossover point.

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.