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Quantum master equation for electron transport through quantum dots and single molecules

A quantum master equation (QME) is derived for the many-body density matrix of an open current-carrying system weakly coupled to two metal leads. The dynamics and the steady-state properties of the system for arbitrary bias are studied using projection operator techniques, which keep track of number of electrons in the system. We show that coherences between system states with different number of electrons, n, (Fock space coherences) do not contribute to the transport to second order in system-lead coupling. However, coherences between states with the same n may effect transport properties when the damping rate is of the order or faster then the system Bohr frequencies. For large bias, when all the system many-body states lie between the chemical potentials of the two leads, we recover previous results. In the rotating wave approximation (when the damping is slow compared to the Bohr frequencies of the system), the dynamics of populations and the coherences in the system eigenbasis are decoupled. The QME then reduces to a birth and death master equation for populations.