Interplay of exciton or electron transfer and relaxation III. Forgetting details of initial conditions

Owing to the recently proved equivalence between the Time-Convolutionless Generalized Master Equation and the Tokuyama-Mori approaches, one can discuss forgetting details of initial conditions in the electron (exciton) transfer and relaxation problem in the above theories in a unified manner. For a single carrier interacting with a thermodynamic bath in a quite general manner and to second order in the carrier-phonon coupling in the theory for the full carrier density matrix, we are able to prove this phenomenon for any carrier system here provided that the total energy spectrum of the bath is continuous. General conclusions are demonstrated with respect to a system with site off-diagonal coupling of an electron (exciton) to the bath. Connection of the model with the Haken-Strobl-Reineker parametrization in the stochastic Liouville equation model is discussed.