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Condensed Matter > Statistical Mechanics

arXiv:cond-mat/0501696 (cond-mat)
[Submitted on 28 Jan 2005 (v1), last revised 22 Aug 2005 (this version, v3)]

Title:Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method

Authors:T. Koide
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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.
Comments: 10 pages, 1 figure, Final version published in Phys. Rev. E
Subjects: Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Phenomenology (hep-ph); Nuclear Theory (nucl-th)
Cite as: arXiv:cond-mat/0501696 [cond-mat.stat-mech]
  (or arXiv:cond-mat/0501696v3 [cond-mat.stat-mech] for this version)
  https://doi.org/10.48550/arXiv.cond-mat/0501696
Journal reference: Phys.Rev. E72 (2005) 026135
Related DOI: https://doi.org/10.1103/PhysRevE.72.026135

Submission history

From: Tomoi Koide [view email]
[v1] Fri, 28 Jan 2005 09:49:09 UTC (14 KB)
[v2] Mon, 27 Jun 2005 18:55:16 UTC (15 KB)
[v3] Mon, 22 Aug 2005 15:41:30 UTC (15 KB)
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