Fermi golden rule, validity

Not only is the master equation more convenient for mathematical operations than the original Chapman-Kolmogorov equation, it also has a more direct physical interpretation. The quantities W(y y ) At or Wnn> At are the probabilities for a transition during a short time At. They can therefore be computed, for a given system, by means of any available approximation method that is valid for short times. The best known one is time-dependent perturbation theory, leading to Fermi s Golden Rule f)... 

The complete derivation of Eq. (6.71) is omitted here because there is no point in proving again the validity of Fermi s Golden Rule (see previous section). For details see ref. [15]. 

J uj) can be assumed to be a smooth function determined by few parameters. These parameters can be determined from a classical molecular dynamics simulation. Once one knows J uj) and V, one can calculate all the properties for the spin-boson system. As a matter of fact, the parameter V is not very important it appears only in a prefactor which multiplies the electron transfer rate. The simple dependence results from an application of Fermi s golden rule, an approximation which appears to be valid in case of electron transfer [7j. 

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