We give a quantum description of a Quantum Electro-Mechanical
System (QEMS) comprising a single quantum dot harmonically bound
between two electrodes and facilitating a tunnelling current
between them. An example of such a system is a fullerene molecule
between two metal electrodes. 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, and give a semiclassical description of the dynamics under a variety of bias conditions. This dynamical description is related to observable features of the system including the stationary conductance as a function of bias voltage.
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