The influence of a constant and thermally activated relaxation rate

4 The influence of a constant and thermally activated relaxation rate 

There are different attempts to link the high-temperature T 10 K) with the low-temperature properties of disordered solids [13, 14]. In particular, it has been proposed that the maximum in the attenuation of phonons observed in amorphous materials at T 10 K can be interpreted assuming a thermally activated relaxation of the two-level systems. In this Section we discuss the influence of thermally activated relaxation rate on the heat release for a finite cooling rate. 

For a single activation barrier Vq between the two potential wells and at a measuring temperature Tq the thermally activated relaxation rate is given by 

Taking into accoimt this relaxation rate in addition to quantum tunneling (Eq. 6) and assuming that both processes are independent, the total relaxation rate can be written as 

To take into account the distribution of potential barriers V and a thermally activated rate we will follow the approach used by Tielbiirger et al. [11] and transform Eq. 11 in a double integral in the variables A and Fusing the approximation A = VlEo and A as lEo T ln  

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