Macroscopic diffusion from a Hamilton-like dynamics
Abstract
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of Hamiltonian dynamics in a confined phase space : it is deterministic, periodic, reversible and conservative. Randomness enters the model as a way to model ignorance about initial conditions and interactions between the components of the system. The orbits of the particles are non-intersecting random loops. We prove, by a weak law of large number, the validity of a diffusion equation for the macroscopic observables of interest for times that are arbitrary large, but small compared to the minimal recurrence time of the dynamics.
Cite
@article{arxiv.1211.0608,
title = {Macroscopic diffusion from a Hamilton-like dynamics},
author = {Raphael Lefevere},
journal= {arXiv preprint arXiv:1211.0608},
year = {2015}
}
Comments
typos corrected, figure improved