Location WB 144, Wallberg Building, 184-200 College Street

In this talk I will present my recent result about ergodic properties of some statistical mechanics models. I will first show that a simple Kac-like interacting particle system has polynomial speed of convergence to its equilibrium, and introduce the method of proof. Similar approach is then applied to a nonequilibrium energy exchange model that is reduced from a billiards-like deterministic particle system, which models the microscopic heat conduction in a 1D chain. I proved the existence, uniqueness, polynomial speed of convergence to the NESS, and polynomial speed of mixing for this stochastic energy exchange model. These results are consistent with the numerical simulation results of the original deterministic billiards-like system.