Librational spectral function Librator dipoles

In this chapter, dielectric response of only isotropic medium is considered. However, in a local-order scale, such a medium is actually anisotropic. The anisotropy is characterized by a local axially symmetric potential. Spatial motion of a dipole in such a potential can be represented as a superposition of oscillations (librations) in a symmetry-axis plane and of a dipole s precession about this axis. In our theory this anisotropy is revealed as follows. The spectral function presents a linear combination of the transverse (K ) and the longitudinal (K ) spectral functions, which are found, respectively, for the parallel and the transverse orientations of the potential symmetry axis with... 

In the second period, which was ended by review GT after the average perturbation theorem was proved, it became possible to get the Kubo-like expression for the spectral function L(z) (GT, p. 150). This expression is applicable to any axially symmetric potential well. Several collision models were also considered, and the susceptibility was expressed through the same spectral function L(z) (GT, p. 188). The law of motion of the particles should now be determined only by the steady state. So, calculations became much simpler than in the period (1). The best achievements of the period (2) concern the cone-confined rotator model (GT, p. 231), in which the dipoles were assumed to librate in space in an infinitely deep rectangular well, and applications of the theory to nonassociated liquids (GT, p. 329). 

In accord with the planar libration approximation, we first come from representation of the spectral function for motion of a dipole in a plane, where integration over l is lacking by definition, so only integration over energy h is employed. We shall find in this way the function (203). As a next step we carry out integration over l, so that a rather simple expression (171) for the spectral function L(z) will be obtained. 

Assumptions 1 and 2 constitute the planar libration-regular precession approximation. In Gaiduk et al. [56] and in GT2 the corresponding spectral functions L(z) and L(z) are found in analytical form, as well as the SF L(z) for the rotators. These SFs are expressed as simple integrals from elementary functions over the full energy of a dipole. The total spectral function is thus represented as... 

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