Differential recurrence relations for the Fokker-Planck equation for magnetic after-effect and dielectric relaxation in non-axially symmetric potentials

The study of the magnetic after-effect behaviour of fine ferromagnetic particles and the dielectric relaxation of polar molecules in the nematic liquid crystalline phase in general requires one to solve the Fokker-Planck equation for the density of dipole moment orientations, in spherical polar coordinates in the presence of a non axially symmetric potential. This amounts to reducing that equation to a set of differential recurrence relations which may be written as an infinite set of simultaneous first order linear differential equations with constant coefficients. A systematic method of deriving the set of differential recurrence relations from the Fokker-Planck equation using the properties of the normalised spherical harmonics is presented. The method is illustrated by considering the magnetic relaxation in an external field which is applied at an angle to the polar axis. The results are in agreement with those obtained by averaging the Langevin equation using the properties of the Stratonovich stochastic calculus.