Spectral gaps in vibrational systems: I. Saxon-Hunter-type theorems in some mixed crystals of the alkali halide type

Abstract

A new method of investigating the problem of spectral gaps in the spectra of disordered lattices is presented, which is very general and not only free from any dimensional restriction but also does not depend on any special assumption concerning the dynamical structure of the lattice, provided only that the interactions are harmonic. By this `evaporation method', it is shown that for the vibrational frequency spectra of some mixed crystals of the alkali halide type, the Saxon-Hunter-type theorem is valid for all the expected spectral gaps, that is, each of the possible common gaps of the constituent regular lattices gives at the same time a gap of the mixed lattice.