Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method
Statistical Mechanics
2009-11-11 v3 High Energy Physics - Phenomenology
Nuclear Theory
Abstract
We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation is consistent with causality and the sum rule associated with the number conservation in the low momentum limit, in contrast to usual acausal diffusion equations given by using the Fick's law. After employing the Markov approximation, we find that the equation has the similar form to the causal diffusion equation. Our result suggests that current-current correlations are not necessarily adequate as the definition of diffusion constants.
Cite
@article{arxiv.cond-mat/0501696,
title = {Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method},
author = {T. Koide},
journal= {arXiv preprint arXiv:cond-mat/0501696},
year = {2009}
}
Comments
10 pages, 1 figure, Final version published in Phys. Rev. E