Fast-Time Heat Capacity in Amorphous Si${\mathrm{O}}_2$ Using Heat-Pulse Propagation

We have performed heat-pulse propagation measurements in amorphous Si${\mathrm{O}}_2$ over the temperature range 50 mK to 3.8 K on the submicrosecond time scale (some two to three orders of magnitude faster than previous measurements). No evidence for deviations from the dc heat capacity have been observed at low temperatures. Between 1 and 2 K, we see evidence for "ballistic" phonon propagation, induced by saturation of the scattering centers.