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.
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Acknowledgements
I thank Jean Bricmont and Carlos Mejia-Monasterio for discussions. This work was supported by the ANR SHEPI grant.
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Lefevere, R. Macroscopic Diffusion from a Hamilton-like Dynamics. J Stat Phys 151, 861–869 (2013). https://doi.org/10.1007/s10955-013-0738-4
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DOI: https://doi.org/10.1007/s10955-013-0738-4