Fixed axis rotation model dielectric relaxation

In the fixed axis rotation model of dielectric relaxation of polar molecules a typical member of the assembly is a rigid dipole of moment p rotating about a fixed axis through its center. The dipole is specified by the angular coordinate < ) (the azimuth) so that it constitutes a system of 1 (rotational) degree of freedom. The fractional diffusion equation for the time evolution of the probability density function W(4>, t) in configuration space is given by Eq. (52) which we write here as... 

The behavior of the dielectric spectra for the two-rotational-degree-of-ffeedom (needle) model is similar but not identical to that for fixed-axis rotators (one-rotational-degree-of-fireedom model). Here, the two- and one-rotational-degree-of-freedom models (fractional or normal) can predict dielectric parameters, which may considerably differ from each other. The differences in the results predicted by these two models are summarized in Table I. It is apparent that the model of rotational Brownian motion of a fixed-axis rotator treated in Section IV.B only qualitatively reproduces the principal features (return to optical transparency, etc.) of dielectric relaxation of dipolar molecules in space for example, the dielectric relaxation time obtained in the context of these models differs by a factor 2. 

The first objective of this review is to describe a method of solution of the Langevin equations of motion of the itinerant oscillator model for rotation about a fixed axis in the massive cage limit, discarding the small oscillation approximation in the context of dielectric relaxation of polar molecules, this solution may be obtained using a matrix continued fraction method. The second... 

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