Adiabatic change in the Smoluchowski equation: Orientational diffusion of polar particles

A system described by a Smoluchowski equation in configuration space is subject to slow change of external fields. The distribution function is studied by expanding it in instantaneous eigenfunctions of the adjoint Smoluchowski operator leading to an adiabatic approximation for the distribution function which is linear in the rates of change of external fields. The general result is applied to a magnetic dipole subject to slowly changing external magnetic field. Both eigenvalues and eigenfunctions are obtained analytically by a series expansion method. For slow change of field magnitude, the eigenfunction solution is compared numerically with the adiabatic approximation and with an independent numerical solution of the Smoluchowski equation. The case of slow rotation of a field of constant magnitude and an example of cyclic change involving both change of magnitude and direction of the field are studied. Significant nonequilibrium components of magnetization are generated and persist throughout the duration of slow change of external field. For the system to be regarded as in thermal equilibrium in the instantaneous external field, the rate of change of the external field must be very much slower than the intrinsic decay rates of the system. (C) 2003 American Institute of Physics.