Time-convolutionless generalized master equations and phonon-assisted hopping

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Abstract
A new time-independent projection formalism has recently been applied to the study of phonon-assisted hopping in amorphous semiconductors using the time-convolution master equations. A negative result was obtained with regards to the possibility of deriving the usual Markoffian rate equations working exactly up to infinite order in the electron-phonon coupling constant g, i.e. keeping finite values of g throughout the calculations. The formalism is applied here to the time-convolutionless master equations with the same result : a proof is given that working exactly up to infinite order, no possibility exists of deriving the rate equations currently used as a starting point in theories of the phonon-assisted hopping although in second order in g, their formal derivation seems to be at hand and straightforward