Sub-exponential mixing of random billiards driven by thermostats

Abstract

We study the class of open continuous-time mechanical particle systems introduced in the paper by Khanin and Yarmola [Ergodic Properties of Random Billiards Driven by Thermostats. Commun. Math. Phys. 320, no. 1, 121-147 (2013)]. Using the discrete-time results from that paper we demonstrate rigorously that, in continuous time, a unique steady state exists and is sub-exponentially mixing. Moreover, all initial distributions converge to the steady state and, for a large class of initial distributions, convergence to the steady state is sub-exponential. The main obstacle to exponential convergence is the existence of slow particles in the system.

References in corpus (2)

• A Model of Heat Conduction
• Controllability for chains of dynamical scatterers

Cited by in corpus (5)

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• Sub-exponential mixing of open systems with particle-disk interactions
• Numerical simulation of polynomial-speed convergence phenomenon
• Stochastic Perturbations of Convex Billiards