Force on a moving point impurity due to quantum fluctuations in a Bose-Einstein condensate

TL;DR

This paper derives an analytical expression for the force exerted on a moving impurity in a Bose-Einstein condensate due to quantum fluctuations, showing it exists at any flow speed below the critical velocity and is proportional to the flow speed.

Contribution

The paper provides the first analytical formula for the force on a point impurity caused by quantum fluctuations in a BEC at zero temperature.

Findings

Force exists at any flow velocity below critical velocity

Force is directly proportional to flow speed

Force arises from scattering of quantum fluctuations

Abstract

An analytic expression is derived for a force on a weak point impurity arising from the scattering of quantum fluctuations in a slow-moving, weakly interacting, three-dimensional Bose-Einstein condensate at zero temperature. In an infinitely extended geometry, this force is shown to exist at any arbitrarily small flow velocity below Landau's critical velocity. Furthermore, this force is shown to be directly proportional to the flow speed.