The non-equilibrium dynamics of trapped ultracold atomic gases, or mixtures thereof, is an extremely rich subject. Despite 20 years of studies, and remarkable progress mainly on the experimental front, numerous open question remain, related to the growth, relaxation and thermalisation of such systems, and there is still no universally-accepted theory for their theoretical description. In this paper we discuss one of the state-of-the-art kinetic approaches, which gives an intuitive picture of the physical processes happening at the microscopic scale, being broadly applicable both below and above the critical region (but not within the critical region itself). Specifically, the Zaremba-Nikuni-Griffin (ZNG) scheme provides a self-consistent description of the coupling between the condensate and the thermal atoms, including the collisions between these two subsystems. It has been successfully tested against experiments in various settings, including collective modes (e.g. monopole, dipole and quadrupole modes), topological excitations (solitons and vortices) and surface evaporative cooling. Here, we show that it can capture two important aspects of non- equilibrium dynamics for both single-component and two-component BECs: the Kohn mode (the undamped dipole oscillation independent of interactions and temperature) and (re)thermalization leading to condensate growth following sudden evaporation. Our simulations, performed in a spherically-symmetric trap reveal (i) an interesting two-stage dynamics and the emergence of a prominent monopole mode in the evaporative cooling of a single component Bose gas, and (ii) the long thermalization time associated with the sympathetic cooling of a realistic two-component mixture. Related open questions arise about the mechanisms and the nature of thermalization in such systems, where further controlled experiments are needed for benchmarking.
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