Master equation for nonstationary states of an electron interacting with phonons

Abstract

We consider the dissipative effects of electron-phonon interactions on electron states which are not eigenstates of the pure electron hamiltonian. A master-equation formalism is developed to calculate the time evolution of the occupation probabilities of these states as well as other elements of the reduced single-electron density matrix. Conditions are found which ensure that the master equations are markoffian. It is suggested that markofficity rather than approximate stationarity is the important criterion for the usefulness of a basis of states for the description of the evolution of a physical system.