Polaron in the dilute critical Bose condensate

TL;DR

This paper investigates the behavior of an impurity in a dilute Bose gas near the critical temperature, revealing non-analytic spectral features and divergence in effective mass and residue.

Contribution

It provides a leading-order calculation of polaron energy and damping rate near the phase transition using the 1/N-expansion, highlighting non-perturbative effects.

Findings

Effective mass diverges logarithmically in the long-length limit.

Quasiparticle residue vanishes logarithmically, indicating non-pole Green's function.

Impurity spectrum exhibits non-analytic behavior near criticality.

Abstract

The properties of impurity immersed in the dilute $D$-dimensional Bose gas at temperatures close to the second-order phase transition point are considered. Particularly by means of the $1/N$-expansion we calculated the leading-order polaron energy and the damping rate in the limit of vanishing boson-boson interaction. It is show that the perturbative effective mass and the quasiparticle residue diverge logarithmically in the long-length limit signalling the non-analytic behavior of impurity spectrum and a non-pole structure of a polaron Green's function in the infrared region, respectively.