Ergodic properties of many particle systems with random external collisions.

Presented by Alexander Lykov - Lomonosov Moscow State University, Russia

Abstract: In the talk we will introduce Hamiltonian particle systems with quadratic potential in which only few degrees of freedom interact with external medium. This interaction is carried out by “collisions”. The meaning of “collision” is quite general in our framework. The main point is that the interaction occurs at random time moments t_1<t_2<… and the given degrees of freedom are transformed “randomly” by some nonlinear (in general) map. Particular cases are: velocity flip (change the momentum sign of the one degree of freedom), one-dimensional collision, two-dimensional collision, etc.. We will formulate several results about convergence to equilibrium for those models; discuss the main steps of the proof. The talk is based on the series of author’s papers (jointly with Malyshev V. ).