A simple example of anomalous diffusion

Claude Aslangul

Physica A: Statistical Mechanics and its Applications, 1996, vol. 226, issue 1, 152-167

Abstract: The motion of a particle confined within a strip (“flat pipe”) with diffusely-reflecting walls is analyzed in detail and provides a simple example of the interplay between randomness and geometrical constraint. The mean square dispersion Δx2 of the position is exactly found in various cases, allowing for a detailed asymptotic analysis. For elastic bounces, Δx2 is shown to behave as t2/ln t at large times, with logarithmic corrections. This anomalous behaviour is rather robust in the sense that it still occurs for thermal bounces. On the other hand, when the particle has a high probability to emerge from a bounce with a very small velocity, Δx2 follows various anomalous time behaviours which, nevertheless, are always superdiffusive.

Keywords: Stochastic processes; Disordered systems (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:226:y:1996:i:1:p:152-167

DOI: 10.1016/0378-4371(95)00330-4

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