Diffusion within a sphere; a non-Gaussian statistical model for particle displacements in a dense colloidal suspension

The diffusive motion of a particle within a spherical volume is analysed in detail, to provide insight into the recently observed non-Gaussian statistical properties of the displacements of particles in a dense colloidal suspension. The intermediate scattering function is evaluated and used as a generating function to provide information about the statistical properties of particle's displacement at all times. Representative numerical results are also presented. The analogous one- and two-dimensional calculations for a particle diffusing on a linear interval and a circular disc are also presented, both for completeness and (in the 1-d case) to demonstrate the principles of the calculation, unburdened by excessive algebraic detail.