2014/04/30 by Giada Basile, Alessia Nota, Federica Pezzotti +1 · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP #math.PR #msc:82B40 #msc:82C05
paper · pdf · doi:10.1007/s00220-015-2306-z
published as Comm. Math. Phys. 336, 1607-1636 (2015) · 33 pages, 7 figures
arxiv created 2016/04/13 · arxiv updated 2016/04/14
We consider the Lorentz model in a slab with two mass reservoirs at the boundaries. We show that, in a low density regime, there exists a unique stationary solution for the microscopic dynamics which converges to the stationary solution of the heat equation, namely to the linear profile of the density. In the same regime the macroscopic current in the stationary state is given by the Fick's law, with the diffusion coefficient determined by the Green-Kubo formula.