  Based on the Langevin equation, a stochastic formulation is implemented to
describe the dynamics of a trapped ion in a bath of ultracold atoms, including
an excess of micromotion. The ion dynamics is described following a hybrid
analytical-numerical approach in which the ion is treated as a classical
impurity in a thermal bath. As a result, the ion energy's time evolution and
distribution are derived from studying the sympathetic cooling process.
Furthermore, the ion dynamics under different stochastic noise terms is also
considered to gain information on the bath properties' role in the system's
energy transfer processes. Finally, the results obtained from this formulation
are contrasted with those obtained with a more traditional Monte Carlo
approach.
