The standard tunneling model with infinite cooling rate

2 The standard tunneling model with infinite cooling rate 

If N two-level systems are in thermal equilibrium at a temperature Ti and they are cooled to To with infinite cooling rate, i. e. the time to cool the sample from to To is zero, from Eq. 2 we obtain 

The standard tunneling model assimies that at low temperatures (T 2 K) the one-phonon process is the dominating mechanism. The one-phonon relaxation rate is given by 

Furthermore, the standard tunneling model assumes that the distribution function of TS is constant in terms of two independent variables, namely the asymmetry A and the tunneling parameter 1, i. e. 

According Ref. [7] the distribution function can be written in terms of the variables E and u as 

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