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.
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