Diagrammatic calculation of energy spectrum of quantum impurity in degenerate Bose-Einstein condensate

TL;DR

This paper develops a diagrammatic perturbation theory to calculate the energy spectrum of an impurity in a Bose-Einstein condensate, providing a detailed dispersion relation and effective mass beyond traditional approximations.

Contribution

It introduces a novel diagrammatic approach for impurity Green's function in a BEC, enabling calculation of energy spectrum and effective mass beyond Golden rule approximation.

Findings

Derived the impurity dispersion relation in BEC

Evaluated the impurity effective mass beyond Golden rule

Developed a diagrammatic perturbation framework

Abstract

In this paper we considered a quantum particle moving through delute Bose-Einstein condensate at zero temperature. In our formulation the impurity particle interacts with the gas of uncoupled Bogoliubov's excitations. We constructed the perturbation theory for the Green's function of the impurity particle with respect to the impurity-condensate interaction employing the coherent-state path integral approach. The perturbative expansion for the Green's function is resumed into the expansion for its poles with the help of the diagrammatic technique developed in this work. The dispersion relation for the impurity clothed by condensate excitations is obtained and effective mass is evaluated beyond the Golden rule approximation.