The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
We consider the mirrors model in a finite d-dimensional domain and connected to particles reservoirs at fixed chemical potentials. The dynamics is purely deterministic and non-ergodic. We study the macroscopic current of particles in the stationary regime. We show that when the size of the system goes to infinity, the behaviour of the stationary current of particles is governed by the proportion of orbits crossing the system. Using this approach, it is possible to give a rigorous proof Fick’s law in a simplified version of the mirrors model in high-dimension. In the mirrors model itself, the Kozma-Sidoravicius argument shows that Fick’s law does not hold in two dimensions. Numerical simulations indicate the validity of Fick’s law in three dimensions and above.
Raphael Lefevere received his Ph.D. in Mathematical Physics from the University of Louvain (Belgium) in 1999. He went on to conduct postdoctoral research at the University of Helsinki (Finland) and in Kyoto University (Japan) before joining the Probability and Stochastic Models Laboratory in Paris Diderot University (France) in 2004. His main research focus is on Statistical Mechanics.