1212.0959 (B. Marcos)

Collisional relaxation of two-dimensional gravitational systems    [PDF]

B. Marcos

Systems with long range interactions present generically the formation of quasi-stationary long-lived non-equilibrium states. These non-Boltzmann states relax to Boltzmann equilibrium following a dynamic which is not well understood. In this letter we derive a simple approximate kinetic equation for the relaxation process in a two-dimensional inhomogeneous self-gravitating particle system, obtaining a Fokker -- Planck equation for the velocity distribution with explicit analytical diffusion coefficients. Performing molecular dynamics simulations using the full dynamics and comparing them with the evolution predicted by the Fokker -- Planck equation, we observe a good agreement with the model for all the duration of the relaxation, from the formation of the Quasi-Stationary state to thermal equilibrium. During all this process we observe a scaling of the relaxation time proportional to the number of particles in the system.

View original: http://arxiv.org/abs/1212.0959