DIFFERENTIAL RECURRENCE RELATIONS FOR THE FOKKER-PLANCK EQUATION FOR MAGNETIC AFTER-EFFECT AND DIELECTRIC-RELAXATION IN NON-AXIALLY SYMMETRICAL POTENTIALS

The study of the magnetic after-effect behaviour of fine ferromagnetic particles and the dielectric relaxation of polar molecules in the nem atic liquid crystalline phase in general requires one to solve the Fok ker-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 differe ntial recurrence relations which may be written as an infinite set of simultaneous first order linear differential equations with constant c oefficients. A systematic method of deriving the set of differential r ecurrence relations from the Fokker-Planck equation using the properti es of the normalised spherical harmonics is presented. The method is i llustrated by considering the magnetic relaxation in an external field which is applied at an angle to the polar axis. The results are in ag reement with those obtained by averaging the Langevin equation using t he properties of the Stratonovich stochastic calculus.