TO-LO splittings of glassy dielectrics

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Abstract
The dielectric function of a glassy dielectric is shown to be expressed in terms of the local density of states and the average of the squared polarization vector. In this expression the Coulomb interaction between arbitrary distant points are taken into account through what we call the dipole approximation. We propose an effective Hamiltonian in which the long-wavelength optic modes are separated from the other vibrational modes, and from which we gain insight into the nature of TO and LO vibrational modes in glassy dielectrics.