Inertial effects in the anomalous dielectric relaxation of rotators in space

The linear dielectric response of an assembly of noninteracting linear (needlelike) dipole molecules (each of which is free to rotate in space) is evaluated in the context of fractional dynamics. The infinite hierarchy of differential-recurrence relations for the relaxation functions appropriate to the dielectric response is derived by using the underlying inertial fractional Fokker-Planck (fractional Klein-Kramers) equation. On solving this hierarchy in terms of continued fractions (as in the normal rotational diffusion), the complex dynamic susceptibility is obtained and is calculated for typical values of the model parameters. It is shown that the model can reproduce nonexponential anomalous dielectric relaxation behavior at low frequencies $(\omega \tau <~1,$ where τ is the Debye relaxation time) and the inclusion of inertial effects ensures that optical transparency is regained at very high frequencies (in the far infrared region) so that Gordon’s sum rule for integral dipolar absorption is satisfied.