# Behavior of the impurity atom in a weakly-interacting Bose gas

## TL;DR

This paper investigates the behavior of a single impurity atom in a dilute Bose condensate, analyzing its spectrum, damping, and stability using perturbation theory, providing insights into impurity dynamics in quantum gases.

## Contribution

It introduces a perturbative approach to calculate impurity spectrum and self-energy in a weakly-interacting Bose gas, including stability analysis for attractive and repulsive polarons.

## Key findings

- Calculated impurity spectrum and damping as functions of momentum.
- Derived self-energy expressions for polarons in the long-wavelength limit.
- Examined impurity stability in the weakly-interacting Bose gas.

## Abstract

We studied the properties of a single impurity atom immersed in a dilute Bose condensate at low temperatures. In particular, we perturbatively obtained the momentum dependence of the impurity spectrum and damping. By means of the Brillouin-Wigner perturbation theory we also calculated the self-energy both for attractive and repulsive polaron in the long-wavelength limit. The stability problem of the impurity atom in a weakly-interacting Bose gas is also examined.