Generation of non-Maxwell-Boltzmann energy distributions during thermalization of interacting baths

We report on numerical experiments of thermalization between two reservoirs in which interspecies interactions are mediated via a Hamiltonian with a Gaussian dependence upon the distance between the particles. By using relatively high statistics, we are able to study deviations from the initially imprinted Maxwell-Boltzmann energy distributions as a function of the range and strength of the interaction, as well as the parameters of the two baths such as masses, trapping frequencies, that strongly affect the spatial overlap of the two species. At large interaction strengths and for any range, deviations are attributable to the sudden conversion of latent interaction energy into kinetic energy of the particles. In addition, long range interactions generate deviations even for interaction strengths in the weak regime, and non-uniform confinement introduces a further source of deviation from the Maxwell-Boltzmann energy distribution. This latter results in transient two temperature Maxwell-Boltzmann distributions suggestive of an inverse cascading route from inter-particle dynamics to thermalization. In the weakly-interacting regime, a simple expression for the equilibrium temperature is also obtained and discussed. These findings may be of relevance in the dynamics of exothermic chemical reactions, in the physics of ultracold atomic mixtures, and in self-sustained burning plasmas.