Diffusion in disordered systems: Effect of short and long range interactions

Armin Bunde

Physica A: Statistical Mechanics and its Applications, 1990, vol. 168, issue 1, 536-545

Abstract: We review recent results for diffusion in disordered systems, where the mobile particles are coupled by hard-core, nearest neighbor, or Coulomb interactions. Specifically, we consider linear chains with local disorder, fractal structures, and two-component random mixtures close to the critical concentration. Due to long-range interactions, the mean square displacement of a tagged particle is described by a new exponent k′ at intermediate time scales t1⪡t⪡t2, 〈r2(t)〉∼tk′. With increasing strength of interaction (decreasing temperature), k' decreases and the crossover time t2 is enhanced. The frequency dependent conductivity scales as σ(ω)∼ωn′, n′=1−k′, at intermediate frequencies. In agreement with the experimental situation, n′ can be considerably larger than the exoponent n=1−k for non-interacting particles. In contrast to n, n′ depends on temperature and does not change remarkably above the critical concentration.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:168:y:1990:i:1:p:536-545

DOI: 10.1016/0378-4371(90)90406-I

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