  We consider the open STIRAP problem by formulating it in terms of generalized
Bloch equations. Expressed in this form the resulting Liouvillian matrix is
analyzed in detail. As it turns out, most of the findings of open STIRAP models
can be understood from the spectrum and eigenstates of the Liouvillian matrix.
As a non-hermitian matrix we particularly discuss the mathematical structure of
it by identifying among others the physical meaning of its eigenvectors and the
system's exceptional points. We also discuss the importance of the Liouvillian
gap which normally implies that any state becomes mixed. However, in certain
situations, for example the STIRAP model under influence of spontaneous
emission, a sort of pump term appears in the equations of motion, and its
effect is to counteract the gap induced decay such that coherence may prevail.
As the STIRAP driving is not perfectly adiabatic, we additionally find that for
spontaneous emission the presence of a non-zero Liouvillian gap actually
enhances the success rate of the process. This is thus an example of a
environment assisted physical operation.
