Inertial effects and dipole-dipole coupling

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Abstract
It is indicated how Kramers' equation for the distribution function (in configuration-angular velocity space) underlying the motion of a pair of dipoles compelled to rotate about an axis through their common centre under the influence of their mutual dipole-dipole interaction may be derived. A solution procedure (analogous to that originally given by Brinkman in a discussion of translational brownian movement) for the equation is then set up, whereby the velocity-dependent portion of the distribution function is expressed in terms of two dimensional Hermite polynomials, whence a hierarchy of equations for the Laplace transform of the distribution function in configuration space is obtained. The lowest order approximation to the solution of the hierarchy is taken. This equation is then used to calculate the ensemble averages appropriate to the decay of electric polarization of an assembly of pairs of dipoles (rotating under the influence of their dipole-dipole interaction) following on the removal of a unidirectional electric field. The results yield a denumerable set of relaxation mechanisms for the polarization of the form: and indicate that the distribution functions calculated from the lowest order approximation to the solution of the hierarchy of Brinkman equations are inadequate as a basis for the explanation of the observed far infra-red absorption.