Some comments on fluctuating-elasticity and local oscillator models for anomalous vibrational excitations in glasses

An overview is given on the present status of the theoretical description of vibrational spectra of glasses, as seen by inelastic neutron, X-ray and light (Raman) scattering. Using the language of Greenʹs/response functions the merits and shortcomings of a local oscillator and a generalized elasticity-theory point of view are discussed. It is pointed out that in both cases the interaction of phonons with disorder-induced irregularities leads to Rayleigh scattering (mean free path ℓ ∝ ω− 4) at low enough frequencies and temperatures. In disordered solids at ambient temperature the Rayleigh scattering is usually masqued by Akhiezer-like anharmonic scattering ℓ ∝ ω− 2, but it can be made visible by lowering the temperature. Using a combination of fluctuating-elasticity theory with an incoherent spectrum of local oscillators a fair description of the vibrational spectrum of glassy SiO2 can be achieved.