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arXiv · 1112.4817

Size-independence of statistics for boundary collisions of random walks and its implications for spin-polarized gases

Dominique J. Bicout·Efim Kats·Alexander K. Petukhov·Robert S. Whitney
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Abstract

A bounded random walk exhibits strong correlations between collisions with a boundary. For an one-dimensional walk, we obtain the full statistical distribution of the number of such collisions in a time t. In the large t limit, the fluctuations in the number of collisions are found to be size-independent (independent of the distance between boundaries). This occurs for any inter-boundary distance, including less and greater than the mean-free-path, and means that this boundary effect does not decay with increasing system-size. As an application, we consider spin-polarized gases, such as 3-Helium, in the three-dimensional diffusive regime. The above results mean that the depolarizing effect of rare magnetic-impurities in the container walls is orders of magnitude larger than a Smoluchowski assumption (to neglect correlations) would imply. This could explain why depolarization is so sensitive to the container's treatment with magnetic fields prior to its use.

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Dominique J. Bicout, Efim Kats, Alexander K. Petukhov, Robert S. Whitney. 2012-10-24. Size-independence of statistics for boundary collisions of random walks and its implications for spin-polarized gases. https://doi.org/10.1103/physrevlett.110.010602

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