Mean field theory of the nonlinear response of an interacting dipolar system withrotational diffusion to an oscillating field

Abstract

A mean field theory of dipolar relaxation in a system of interacting dipoles isdeveloped on the basis of a local field picture. The distribution of orientations of aselected dipole is assumed to satisfy a rotational diffusion equation ofSmoluchowski type with time-dependent potential determined self-consistentlyfrom the mean dipole moment. The response to an oscillating Maxwell field actingin a volume element is studied for arbitrary amplitude and frequency of the field.For weak field the theory is similar to that developed by Debye, who used theLorentz local field factor, and derived an expression for the frequency-dependentsusceptibility of Clausius–Mossotti form. In the present theory the local fieldfactor is found from the static linear response in thermal equilibrium. The samelocal field factor is used for strong field. Then the mean dipole moment oscillatesanharmonically, and the maximum absorption shifts to higher frequency.