Inertial effects in anomalous dielectric relaxation

Abstract

The inertia corrected Debye model of rotational Brownian motion of polar molecules is generalized to fractional dynamics (anomalous diffusion) in the context of the fractional Klein-Kramers equation. The fractal generalization of the Gross-Sack solution for the complex dielectric susceptibility ?(?) for an assembly of fixed axis rotators is given. The high-frequency behavior of ?(?) is controlled by the inertia of a dipole as in normal diffusion, so that the Gordon sum rule for dipolar absorption is satisfied ensuring a return to optical transparency at very high frequencies.