Perturbation theory for transition rates in the Pauli equation

Perturbation theory for the transition rates in the Pauli equation 

We consider a subsystem characterized by the states with the energies sa and the rates wqq for transitions from a state q into a state q that satisfy the principle of 

The Pauli equation165 for the probability pq(t) of finding the subsystem in the state q at time t is conveniently written to perform further transformations  

The principle of detailed balance which is also valid for the quantities fVqq- enables the diagonalization of the nonsymmetric matrix Wqq with nonnegative elements  

If we denote the initial probabilities for state occupations at time t=0 by pq(0), the solution of Eq. (4.2.30) takes the following form  

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