perturbation theory. Hence, a theory beyond master equation approach or linear response is necessary. Most of the theoretical work on transport in NEMS has been done within the scattering theory approach (Landauer) but it disregards the contacts and their effects on the scattering channel as well as effect of electrons and phonons on each other $^{23}$. Very recently, the non–equilibrium Green’s function (NEGF) approach 24–26 has been growing in importance in the quantum transport of nanomechanical systems $^{15–18,27,28}$. An advantage of this method is that it treats the infinitely extended reservoirs in an exact way $^{29}$, which may lead to a better understanding of the essential features of NEMS. NEGF has been applied in the study of shot noise in chain models 30 and disordered junctions 31 while noise in Coulomb blockade Josephson junctions has been discussed within a phase correlation theory approach $^{32}$. In the case of an inelastic resonant tunneling structure, in which strong electron-phonon cou- pling is often considered, a very strong source-drain voltage is expected for which coherent electron transport in molecular devices has been considered by some workers 33 within the scattering theory approach. Inelastic effects on the transport properties have been studied in connection with NEMS and substantial work on this issue has been done, again within the scattering theory approach $^{23}$. Recently, phonon assisted resonant tunneling conductance has been discussed within the NEGF technique at zero temperature $^{34}$. To the best of our knowledge, in all these studies, time-dependent quantum transport properties of a resonant tunnel junction coupled to a nanomechanical oscillator have not been discussed so far. The development of time-dependent quantum transport for the treatment of nonequilibrium sys- tem with phononic as well as Fermionic degree of freedom has remained a challenge since the 1980’s $^{35}$. Generally, time-dependent transport properties of mesoscopic systems without nanomechanical oscillator have been reported 36 and, in particular, sudden joining of the leads with quantum dot molecule have been investigated 35,37 for the case of a noninteracting quantum dot and for a weakly Coulomb interacting molecular system. Strongly interacting systems in the Kondo regime have been investigated $^{38,39}$. More recently$^{40}$, the transient ef- fects occurring in a molecular quantum dot described by an Anderson-Holstein Hamiltonian has been discussed. To this end, we present the following study. 

In the present work, we shall investigate the time evolution of a quantum dot coupled to a single vibrational mode as a reaction to a sudden joining to the leads. We employ the non-equilibrium Green’s function method in order to discuss the transient and steady state dynamics of NEMS. This is a fully quantum mechanical formulation whose basic ap- 

