Static impurities in a weakly-interacting Bose gas

Abstract

We present a comprehensive discussion of the ground-state properties of dilute D-dimensional Bose gas interacting with a few static impurities. Assuming the short-ranged character of the boson-impurity interaction, we calculate the energy of three-and two-dimensional Bose systems with one and two impurities immersed.

The effect of boson-boson interaction on the Bipolaron formation

“…Building on the single impurity case, one therefore might expect that the results obtained from the Frölich model for weak couplings can be improved upon in a straightforward way by including higher-order phonon impurity scattering terms. However, we will show that if one proceeds in a naive manner for two impurities, this can lead to unphysical divergences in the ground state energy due to the bound state formation between the two impurities and the excitations of the Bose gas, something that has also been demonstrated in [38]. In contrast to the single impurity case, this occurs for attractive and repulsive impurity-boson scattering lengths.…”

Polaron in almost ideal molecular Bose-Einstein condensate

“…Integrations in S are carried out in large D + 1 'volume' βL D and all three fields are periodic with the period L in every of D spatial directions, and anti-periodic with the period β in the imaginary-time direction. The couplings g and g i are assumed to be conventionally rewritten (see, for instance [48]) through the ↑-fermion-↓-fermion and σfermion-impurity vacuum binding energies, respectively. In principle, the ultraviolet divergences in the two-body sectors can be treated by the dimensional regularization as well.…”

Mobile impurity in a one-dimensional gas at finite temperatures

“…To theoretically explore the properties of a quantum particle propagating in a one-dimensional medium different schemes and approximations were developed. For instance, various mean-field approaches [20][21][22][23][24] can be used to describe properties of the ground state. Instead, perturbation theories for the weak impurity-gas coupling allows one to describe dynamics of the impurity [25][26][27][28][29].…”