Rotational Brownian motion in an external potential: The Langevin equation approach

The theory of orientation relaxation is developed without recourse to the Fokker-Planck equation by direct averaging of the underlying Langevin equation for the noninertial rotational Brownian motion of a polar particle in an arbitrary external potential. Two problems are considered: (i) orientation relaxation of a polar molecule governed by the vector Euler-Langevin equation and (ii) magnetisation relaxation of a single domain ferromagnetic particle described by Gilbert's equation augmented by a random field term. Those equations being regarded as stochastic non-linear differential equations of the Stratonovich type.