Rotational diffusion of a tracer colloid particle

We study the orientational correlations of a tracer colloid particle which carries a magnetic moment. We assume the tracer interacts with other particles in the colloid suspension through spherically symmetric pair potentials and hydrodynamic forces. We derive correlation functions identities arising from the microscopic symmetries of rotation, time translation and time reversal. Using a previously derived cluster expansion representation and assuming there is no external magnetic field we obtain an approximate analytic expression for the two-body contribution to the correlation functions valid for all times. In the case of hard spheres with stick hydrodynamic boundary conditions we evaluate the long time correlation functions numerically to show that, within our approximation, the deviation from single exponential decay is small in a low density suspension.