A note on confined diffusion

Details A note on confined diffusion A note on confined diffusion

2006-04-05

arxiv.org/abs/cond-mat/0604133v2

Physica A 377, 24 (2007)

Physics

Condensed Matter

Statistical Mechanics

10 pages; Eq. (2) corrected

Scientific paper

10.1016/j.physa.2006.11.008

The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion operator. Unfortunately, the latter depend on space dimensionality and on the particular shape of the domain, and an analytical expression is in most circumstances not available. In this article, it is shown that the series may in some circumstances sum up exactly. Explicit calculations are performed for 2D diffusion restricted to a circular domain and 3D diffusion inside a sphere. In both cases, the short-time behaviour of the mean square displacement is obtained.

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