Motion of a heavy impurity through a Bose-Einstein condensate

TL;DR

This paper investigates the motion of a point-like impurity in a Bose-Einstein condensate at zero temperature, calculating the induced mass and drag force across different dimensions using perturbative and exact methods.

Contribution

It provides a comprehensive analysis of impurity dynamics in BECs, combining Gross-Pitaevskii and Lieb-Liniger theories to explore drag forces and induced mass in various dimensions.

Findings

Drag force appears only for supersonic impurity motion in 3D and 2D.

In 1D, drag force exists at arbitrarily small velocities.

Induced mass matches Bogoliubov theory predictions.

Abstract

We study motion of a point-like impurity in a Bose-Einstein condensate at T=0. By solving the Gross-Pitaevskii equation in a perturbative manner we calculate the induced mass of the impurity and the drag force on the impurity in 3D, 2D and 1D cases. The relationship between the induced mass and the normal mass of fluid is found and coincides with the result of the Bogoliubov theory. The drag force appears for supersonic motion of the impurity. In 1D the drag force is investigated also on the basis of the exact Lieb-Liniger theory, using the dynamic form factor, which has been evaluated by the Haldane method of the calculation of correlation functions. In this theory the force appears for an arbitrarily small velocity of the impurity. The possibility of measuring the form factor in existing experiments is noted.