HEAT RELEASE IN GLASSES AT LOW-TEMPERATURES

The long-time heat release in glasses after cooling a sample from some initial temperature T1 to T0 has been calculated in the framework of the soft-potential model. It is shown that there are three temperature regions where time and temperature dependences of the heat release are different. In the thermal activation region T0 > T(c) (where T(c) is a characteristic crossover temperature from tunneling to activation of the order of a few kelvin) the heat release appears to be independent of T1 and proportional to T0(9/4)ln(t/t0)/t almost-equal-to T0(9/4)/t0.76 for t > t0, where t0 is of the order of 100 s. In the tunneling region T1 < T(c) the heat release is proportional to (T1(2)-T0(2))/t in accordance with a prediction of the standard tunneling model. And in the intermediate region T0 < T(c) < T1 the heat release is proportional to (T(c)2-T0(2))/t and does not depend on T1. It is shown that there is a distribution of the characteristic crossover temperature in the glass. This distribution can be calculated from the heat-release data in the intermediate temperature region. The distribution function has several peaks corresponding to several types of two-level systems in the glass. Choosing these distributions it is possible to explain the numerous heat-release experiments in different materials.