Generalized Lyddane-Sachs-Teller relation and disordered solids

Abstract

The realization that the Lyddane-Sachs-Teller (LST) relation can be presented in a particular second-moment representation with the use of only sum rules and causality provides a new way to characterize the electrodynamic response of disordered solids. In this paper we extend this idea in three different directions. (1) The individual second moments of the frequency-dependent transverse and longitudinal dielectric response functions are obtained for the case of multiple dispersion oscillators in high-symmetry crystals, and the generalized LST relation is recovered. (2) The fluctuation-dissipation theorem is used to show the connection between the second moments in ordered or disordered solids and the corresponding mean-square fluctuating polarization densities, thus relating these fluctuations with the generalized LST relation. (3) The moment representation is used to construct a wave-vector-dependent LST relation, applicable when the length scale of the disorder in an isotropic medium is smaller than that of the probing wavelength.