Dynamics of thermalization in classical three-dimensional many-body systems: Non-Maxwellian distributions and the role of anisotropic trapping

The physics of interacting baths is of interest in a variety of contexts, ranging from ultracold atoms to ionized gases. While many features can already be captured in a one-dimensional model, others are specific to the situation of two- or three-dimensional systems. In this paper we focus on three-dimensional features of a model for thermalization between two baths that we have explored in earlier publications. In contrast to the one-dimensional situation we show that, en route to thermalization, deviations from the Maxwell-Boltzmann energy distributions more akin to κ distributions are observed. In three dimensions, these can be seen in changes at the peak of the distribution, which is precluded by the expected monotonic behavior of the energy distributions in one dimension. Furthermore, we consider thermalization for anisotropic trapping and explore its role in the onset of anomalous scaling with respect to the particle number. These results may be pertinent to the understanding of the interplay between turbulent behavior and nonlinearities for a variety of many-body classical systems.