  We describe a quantum electromechanical system(QEMS) comprising a single
quantum dot harmonically bound between two electrodes and facilitating a
tunneling current between them. An example of such a system is a fullerene
molecule between two metal electrodes [Park et al., Nature, 407, 57 (2000)].
The description is based on a quantum master equation for the density operator
of the electronic and vibrational degrees of freedom and thus incorporates the
dynamics of both diagonal (population) and off diagonal (coherence) terms. We
derive coupled equations of motion for the electron occupation number of the
dot and the vibrational degrees of freedom, including damping of the vibration
and thermo-mechanical noise. This dynamical description is related to
observable features of the system including the stationary current as a
function of bias voltage.
