  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.
