Polaron in the dilute critical Bose condensate

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