  Thermalization of a system in the presence of a heat bath has been the
subject of many theoretical investigations especially in the framework of
solid-state physics. In this setting, the presence of a large bandwidth for the
frequency distribution of the harmonic oscillators schematizing the heat bath
is crucial, as emphasized in the Caldeira-Leggett model. By contrast, ultracold
gases in atomic traps oscillate at well-defined frequencies and therefore seem
to lie outside the Caldeira-Leggett paradigm. We introduce interaction
Hamiltonians which allow us to adapt the model to an atomic physics framework.
The intrinsic nonlinearity of these models differentiates them from the
original Caldeira-Leggett model and calls for a nontrivial stability analysis
to determine effective ranges for the model parameters. These models allow for
molecular dynamics simulations of mixtures of ultracold gases, which is of
current relevance for optimizing sympathetic cooling in degenerate Bose-Fermi
mixtures.
