# Fick's law in a random lattice Lorentz gas

Abstract : We provide a proof that the stationary macroscopic current of particles in a random lattice Lorentz gas satisfies Fick's law when connected to particles reservoirs. We consider a box on a d+1 dimensional lattice and when $d\geq7$, we show that under a diffusive rescaling of space and time, the probability to find a current different from its stationary value is exponentially small in time. Its stationary value is given by the conductivity times the difference of chemical potentials of the reservoirs. The proof is based on the fact that in high dimension, random walks have a small probability of making loops or intersecting each other when starting sufficiently far apart.
Type de document :
Pré-publication, Document de travail
2014
Domaine :

https://hal.archives-ouvertes.fr/hal-00984663
Contributeur : Raphael Lefevere <>
Soumis le : lundi 28 avril 2014 - 16:24:16
Dernière modification le : mardi 11 octobre 2016 - 15:20:23

### Identifiants

• HAL Id : hal-00984663, version 1
• ARXIV : 1404.5694

### Citation

Raphael Lefevere. Fick's law in a random lattice Lorentz gas. 2014. <hal-00984663>

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