  We discuss the dynamics of sympathetic cooling of atomic mixtures in
realistic, nonlinear trapping potentials using a microscopic effective model
developed earlier for harmonic traps. We contrast the effectiveness of
different atomic traps, such as Ioffe-Pritchard magnetic traps and optical
dipole traps, and the role their intrinsic nonlinearity plays in speeding up or
slowing down thermalization between the two atomic species. This discussion
includes cases of configurations with lower effective dimensionality. From a
more theoretical standpoint, our results provide the first exploration of a
generalized Caldeira-Leggett model with nonlinearities both in the trapping
potential as well as in the interspecies interactions, and no limitations on
their coupling strength.
