Generation of dispersive shock waves by the flow of a Bose-Einstein condensate past a narrow obstacle

TL;DR

This paper investigates how a Bose-Einstein condensate flowing past a narrow obstacle can generate dispersive shock waves and sonic horizons, with analytical conditions validated by numerical simulations.

Contribution

It provides explicit conditions for the formation of dispersive shock waves and sonic horizons in Bose-Einstein condensate flows, combining analytical derivations with numerical validation.

Findings

Dispersive shock waves form upstream of the obstacle.

A sonic horizon can be generated downstream in the flow.

Analytical predictions match numerical simulations.

Abstract

We study the flow of a quasi-one-dimensional Bose-Einstein condensate incident onto a narrow obstacle. We consider a configuration in which a dispersive shock is formed and propagates upstream away from the obstacle while the downstream flow reaches a supersonic velocity, generating a sonic horizon. Conditions for obtaining this regime are explicitly derived and the accuracy of our analytical results is confirmed by numerical simulations.