Fractional rotational Brownian motion in a uniform dc external field

The longitudinal and transverse components of the complex dielectric susceptibility tensor of an assembly of dipolar particles subjected to a dc bias field are evaluated in the context of a fractional noninertial rotational diffusion model. Exact and approximate solutions for the dielectric dispersion and absorption spectra are obtained. It is shown that a knowledge of the effective relaxation times for normal rotational diffusion is sufficient to predict accurately the anomalous dielectric relaxation behavior of the system for all time scales of interest. Simple equations for the characteristic frequencies of the dielectric loss spectra are obtained in terms of the physical model parameters (dimensionless field and fractional exponent). The model explains the anomalous (Cole-Cole like) relaxation of complex dipolar systems, where the anomalous exponent differs from unity (corresponding to the normal dielectric relaxation), i.e., the relaxation process is characterized by a broad distribution of relaxation times.