Role of thermal two-phonon scattering for impurity dynamics in a low-dimensional Bose-Einstein condensate - Lausch, Tobias; Widera, Artur; Fleischhauer, Michael (Physical Review A, 2018)
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 T2ph. T2ph scales inversely with the system size and is much smaller than currently experimentally accessible.
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