Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate

TL;DR

This paper studies the formation of stationary 3D wave patterns caused by a small impurity moving faster than the speed of sound in a Bose-Einstein condensate, providing asymptotic formulas validated by simulations.

Contribution

It derives asymptotic formulas for stationary wave patterns in 3D BECs and confirms their accuracy through numerical simulations.

Findings

Asymptotic formulas accurately describe far-field density patterns

Stationary wave patterns are generated by supersonic impurities in BECs

Formulas are valid at distances of a few wavelengths from the impurity

Abstract

Formation of stationary 3D wave patterns generated by a small point-like impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at distances from the obstacle equal to a few wavelengths.