Quasi-stationary states in particle systems with power law interactions

by Michael Joyce (UPMC Univ Paris 06, UMR 7585, LPNHE, F-75005, Paris, France)

Wednesday 15 Apr 2015, 15:00 → 16:00 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

One of the most basic and interesting features which has been noted of various many particle systems with long-range interactions is that they relax to ``quasi-stationary states”, which are non-equilibrium stationary states of which the lifetime diverges in the thermodynamic limit. I will give a brief review of the theoretical interpretation of these states within the framework of the Vlasov equation. I will then describe recent work, using two different approaches, which addresses the question of how the existence of these states is tied to the nature of the underlying interaction, and in particular to its range as characterised by the rapidity of the decay of the interaction potential at large distances. Both approaches lead to the conclusion, born out by numerical study, that the existence of these states is a robust property only for interactions for which the pair force is integrable at large distances. We argue that this motivates a natural and relevant classification of interactions into “dynamically" long and short range which is distinct from the usual thermodynamic one.