Dominique J. Bicout, Efim Kats, Alexander K. Petukhov, Robert S. Whitney
A random walk exhibits strong correlations between subsequent collisions with
a boundary. We study the statistics of the fluctuations in the number of such
collisions, and show that they display universality in the long time limit; the
variances and higher-moments being independent of the distance between
boundaries. This is despite the average number of collisions scaling like one
over the inter-boundary distance. In one-dimension, the universality occurs for
any inter-boundary distance, from the quasi-ballistic to the diffusive regime.
Extending the results to the three-dimensional diffusive regime, we analyze the
depolarization of spin-polarized gases, such as 3He. We find boundary-induces
depolarization processes which are independent of the container size. Our
theory gives a model of why the depolarization rate for containers with
magnetic impurities in their walls is extremely sensitive to the treatment of
containers with magnetic fields before use.
View original:
http://arxiv.org/abs/1112.4817
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