  We investigate the effect of quantisation of vibrational modes on a system in
which the transport path is through a quantum dot mounted on a cantilever or
spring such that tunnelling to and from the dot is modulated by the
oscillation. We consider here the implications of quantum aspects of the
motion. Peaks in the current voltage characteristic are observed which
correspond to avoided level crossings in the eigenvalue spectrum. Transport
occurs through processes in which phonons are created. This provides a path for
dissipation of energy as well as a mechanism for driving the oscillator, thus
making it easier for electrons to tunnel onto and off the dot and be ferried
across the device.
