Nordita Astrophysics Seminars

Playing billiard and warming up to it

by Thomas Gilbert

Europe/Stockholm
122:026

122:026

Description

With the motivation to study transport processes such as diffusion of mass or heat in mechanical systems, I will describe different classes of (possibly high-dimensional) billiard models. The strategy is to identify a limiting regime of separation between slow and fast degrees of freedom such that the dynamics of the slow variables can be approximated by a Markov process. We are then left with a stochastic law for the slow variables at a mesoscopic scale. Its macroscopic limit is the final goal. While the transport of mass in two-dimensional billiard table offers a rather simple illustration, heat transport, which involves correlations between the many degrees of freedom involved, is trickier. Nonetheless it remains within reach.With the motivation to study transport processes such as diffusion of mass or heat in mechanical systems, I will describe different classes of (possibly high-dimensional) billiard models. The strategy is to identify a limiting regime of separation between slow and fast degrees of freedom such that the dynamics of the slow variables can be approximated by a Markov process. We are then left with a stochastic law for the slow variables at a mesoscopic scale. Its macroscopic limit is the final goal. While the transport of mass in two-dimensional billiard table offers a rather simple illustration, heat transport, which involves correlations between the many degrees of freedom involved, is trickier. Nonetheless it remains within reach.