Role of thermal two-phonon scattering for impurity dynamics in a low-dimensional Bose-Einstein condensate

We numerically study the relaxation dynamics of a single, heavy impurity atom interacting with a finite one-or two-dimensional, ultracold Bose gas. While there is a clear separation of time scales between processes resulting from single- and two-phonon scattering in three spatial dimensions, the thermalization in lower dimensions is dominated by two-phonon processes. This is due to infrared divergences in the corresponding scattering rates in the thermodynamic limit, which are a manifestation of the Mermin-Wagner-Hohenberg theorem. This makes it necessary to include second-order phonon scattering above a crossover temperature T-2ph. T-2ph scales inversely with the system size and is much smaller than currently experimentally accessible.