Resonant phonon scattering in metallic glasses

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Abstract
The two-level systems (TLS) in metallic glasses at low temperatures are so heavily damped by inelastic electron scattering that one cannot realistically describe the resonant absorption of phonons by these systems using Fermi's Golden Rule. A simple idealized model is considered in which both the TLS—phonon and TLS—electron interactions are off-diagonal, and this is analysed to infinite-order perturbation theory using quantum-field techniques. The result for the total phonon scattering rate is almost identical to Fermi's Golden Rule, except that the density of final states is replaced by the spectral density of the TLS. This spectral density cannot be calculated exactly, but consideration of its low-frequency limiting behaviour shows that resonant scattering alone cannot explain the anomalous behaviour in the saturation of the ultrasonic attenuation observed by Araki, Park, Hikata and Elbaum (1979).