Light Induced Transition Probabilities and Rate Equations
One can assume rate constants for the absorption and emission of light quanta and describe ground state and excited state of molecules in a very generalized way. The absorption of photons transfers the system from the electronic ground state N0 to an electronically excited state N1. We can generally assume to have an infinite number of such states. Recalling eq. 4 and eq. 5 we remember that the general master equation that denotes the dynamical formulation of the temporal change of states Nt might be time dependent Nj (t) and is therefore described by a differential equation that denotes the dynamical change in time Nj (t) :
with the transfer matrix Tjk=T. If we separate the supplying processes and the emptying processes we get:
This means that the description of our transfer matrix Tjk=T contains all processes that deliver Nj (t) as off-diagonal elements and the process of the decaying Nj (t) as elements on the matrix diagonal. This description is very suitable to calculate time dependent spectra that result from fluorescence decay.
The full master equation denotes to
where the diagonal of the transfer matrix is filled with zeros. A generalized description of the motivation of the master equation was given in chapter 1.3 and can be reviewed in (Haken, 1990) and (Schmitt, 2011).