Classical diffusion in presence of geometrical constraints and/or interactions

  • C. Aslangul
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 519)


Geometrical constraints, boundary conditions and interactions are expected to modify standard classical random motion. Two examples are given: (i) motion of a particle in a long narrow pipe, which can be viewed as a sequence of clusters of small erratic steps separated by long-distance jumps, strongly reminiscent of a Lévy walk at least on a pictorial level. (ii) 1d diffusion of a set of N particles with a hard-core contact interaction. In the first case, according to the nature of the bounces (elastic random, thermal, soft…), the mean square dispersion displays a large variety of asymptotic behaviours: t 2/ln t, t μ … In most cases, the behaviour is superdiffusive; For the N interacting particles on the line, the k th moment of the one-body reduced coordinate distributions behaves as t k/2 at all times. In particular, although ordinary diffusion always occurs, the diffusion constant D strongly depends in a non-intuitive way upon the number N of interacting particles; for the borderline particle, D(N) decreases as 1/ln N whereas for the central one, D(N) decreases as N −1.


Diffusion Constant Asymmetric Simple Exclusion Process Ordinary Diffusion Edge Particle Narrow Pipe 
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Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • C. Aslangul
    • 1
  1. 1.Groupe de Physique des SolidesUniversités Paris 7 et Paris 6Paris Cedex 05France

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