We study the diffusion of Brownian particles on the surface of a sphere and
compute the distribution of solid angles enclosed by the diffusing particles.
This function describes the distribution of geometric phases in two state
quantum systems (or polarised light) undergoing random evolution. Our results
are also relevant to recent experiments which observe the Brownian motion of
molecules on curved surfaces like micelles and biological membranes. Our
theoretical analysis agrees well with the results of computer experiments.Comment: 11 pages, two figures, Fig2 in Colour,references update
