Size Independence of Statistics for Boundary Collisions of Random Walks and Its Implications for SpinPolarized Gases
Abstract
A bounded random walk exhibits strong correlations between collisions with a boundary. For a onedimensional 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 interboundary distance, from less to greater than the mean free path, and means that this boundary effect does not decay with increasing system size. As an application, we consider spinpolarized gases, such as 3helium, in the threedimensional 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.
 Publication:

Physical Review Letters
 Pub Date:
 January 2013
 DOI:
 10.1103/PhysRevLett.110.010602
 Bibcode:
 2013PhRvL.110a0602B
 Keywords:

 05.40.Fb;
 67.30.ep;
 76.60.k;
 Random walks and Levy flights;
 Spin polarized <sup>3</sup>He;
 Nuclear magnetic resonance and relaxation