W.T. Coffey, Yu.P. Kalmykov and S.V. Titov, 'Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields' in Journal of Chemical Physics, 126, (2007), pp 084502-1 - 084502-6
Journal of Chemical Physics 126
It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.
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