Motion of quantum particle in dilute Bose-Einstein condensate at zero temperature

TL;DR

This paper investigates the motion and dissipation of a quantum particle in a zero-temperature Bose-Einstein condensate using perturbation theory, Bogoliubov's method, and analyzes energy dissipation and effective mass.

Contribution

It introduces a perturbative approach to analyze impurity dynamics in BEC, including dissipation rates and energy spectrum evaluation, within a zero-temperature framework.

Findings

Calculated dissipation rate due to excitation creation in BEC.

Reproduced Landau's criterion for energy dissipation.

Evaluated impurity energy spectrum and effective mass.

Abstract

The motion of single quantum particle through Bose-Einstein condensate (BEC) is considered within perturbation theory with respect to the particle-BEC interaction. The Hamiltonian of BEC is diagonalized by means of Bogoliubov's method. The process of dissipation due to the creation of excitation in BEC is analyzed and the dissipation rate is calculated in the lowest order of perturbation theory. The Landau's criterion for energy dissipation in BEC is then recovered. The energy spectrum of the impurity particle due to the interaction with BEC and its effective mass are evaluated.