Measurements of the time-dependent specific heat of amorphous materials

The time dependence of the specific heat of several amorphous materials, such as $a$-Si${\mathrm{O}}_2$, $a$-${\mathrm{As}}_2$ ${\mathrm{S}}_3$, and $a$-As, has been studied in the temperature range 0.1-1 K. It is found that below 0.3 K in all the materials studied the short-time specific heat at about 10 μsec is considerably smaller than the long-time specific heat, but larger than the Debye value. Above 0.3 K most of the specific heat is coupled to the phonons already at 10 μsec. However, measurements at very long time scales reveal that the specific heat has a component with a logarithmic time dependence, as proposed by the tunneling model, although only part of the total specific heat can be ascribed to it.