proximations are very transparent, as the technique has already been used to study trans- port properties in a wide range of systems. In our calculation inclusion of the oscillator is not perturbative as the STS experiments 21,22 are beyond the perturbation theory. So a non-perturbative approach is required beyond the quantum master equation 27,28,41 or lin- ear response. Hence, our work provides an exact analytical solution to the current–voltage characteristics, including coupling of leads with the system, very small chemical potential difference and both the right and left Fermi level response regimes. For simplicity, we use the wide-band approximation $^{25,35,42,43}$, where the density of states in the leads and hence the coupling between the leads and the dot is taken to be independent of energy. Although the method we are using does not rely on this approximation. This provides a way to perform transient transport calculations from first principles while retaining the essential physics of the electronic structure of the dot and the leads. Another advantage of this method is that it treats the infinitely extended reservoirs in an exact way in the present system, which may give a better understanding of the essential features of NEMS in a more appropriate quantum mechanical picture. We consider a single quantum dot connected to two identical metallic leads. A single oscillator is coupled to the electrons on the dot and the applied gate voltage is used to tune the single level of the dot. In the present system, we neglect the spin degree of freedom and electron-electron interaction effects and consider the simplest possible model system. We also neglect the effects of finite electron temperature of the lead reservoirs and damping of the oscillator. Our model consists of the individual entities such as the single quantum dot and the left and right leads in their ground states at zero temperature. The Hamiltonian of our simple system 34,42,43 is II. MODEL CALCULATIONS where ϵ$_{0}$ is the single energy level of electrons on the dot with c † $_{0}$, c$_{0}$ the corresponding creation and annihilation operators, the coupling strength, η = λl, with λ = eE, is the electrostatic field between electrons on the dot and an oscillator, seen by the electrons due to the charge on the oscillator, l = √ ℏ / 2 mω is the zero point amplitude of the oscillator, H$_{dot-ph}$ = [ ϵ$_{0}$ + λl ( b † + b ) ] c † $_{0}$c$_{0}$ + ℏ ω ( b $^{†}$b + 1 $_{2}$) , (1) 4