On the ultrasonic attenuation in glasses at low temperatures

The ultrasonic attenuation in glasses at low temperatures is calculated using the model proposed by Anderson, Halperin, and Varma. It is found that the resonant absorption of sound by the localized two-level systems saturates and can be observed only if the sound amplitude is extremely small. A second contribution to the sound absorption is derived which arises from the relaxation of the localized excitations and does not saturate. Qualitative agreement with recent measurements of the ultrasonic attenuation in fused silica is obtained.