Low temperature acoustic properties of amorphous silica and the tunneling model

Internal friction and speed of sound were measured on a-SiO2 above 6 mK usi ng a torsional oscillator at 90 kHz, controlling for thermal decoupling, vi brational heating, background losses, and nonlinear effects. Strain amplitu des epsilon(A) = 10(-8) mark the transition between the linear and nonlinea r regimes. In the former, agreement with the tunneling model was observed f or both internal friction and speed of sound above 25 mK. The observed devi ations in the speed of sound below 25 mK can be described with a cutoff ene rgy of Delta(0,min)/k(B) = 6 +/- 0.5 mK. In the nonlinear regime, above 10 mK the behavior was typical for nonlinear harmonic oscillators, while below 10 mK different behavior was found.