Analytical solution of the master equation with the transition probability derived from dynamical considerations

An exact relationship between the transition probability P(E → E^′) and quantum transition probabilities P_i→f of an active molecule under the effect of collisions with medium molecules is obtained. Treating an active molecule as a system of harmonic oscillators, it is possible to derive the analytical expression for P(E → E^′) from the “first principles” using the first-order perturbation theory for probabilities P_i→f. The only parameter of the model is expressed in terms of vibrational relaxation time that may be calculated numerically or taken from experiments. For the system of harmonic oscillators placed in a thermal bath, the solution of the master equation is found in the analytical form. An extended discussion of the model is also presented.