Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method

Details Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method

2005-01-28

arxiv.org/abs/cond-mat/0501696v3

Phys.Rev. E72 (2005) 026135

Physics

Condensed Matter

Statistical Mechanics

10 pages, 1 figure, Final version published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.72.026135

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.

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