nanomechanical oscillator is zero for long time. Hence, we conclude that the long time dynamics of the classical mechanical oscillator is always zero. Finally, in fig. 8, we have shown the Fano factor as a function of time for two different values of η = 0 . 02 , η = 0 . 08 and for fixed values of Γ = 0 . 01 , ϵ$_{F}$$_{R}$ = 0 , ϵ$_{F}$$_{L}$ = 1. In the limit of weak coupling, the nanomechanical oscillator shows thermal like behavior and poissonian statistics while in the limit of strong coupling its dynamics is non-thermal which leads to super-poissonian statistics. In this figure, the short time behavior is always thermal, but this is trivial as the nanomechanical oscillator is initially in its ground state. In conclusion, we have found mixed and pure states in our results which confirm the quantum dynamics of our model with the following justifications: in a classical mechanical oscillator model 15–17,47 all states give rise to a time dependent potential. Hence, all states of the classical mechanical oscillator are damped. Thus, we confirm the new quantum dynamics of the nanomechanical oscillator that will be helpful for further experiments beyond the classical limit to develop better understanding of NEMS devices. FIG. 8. Fano factor as a function of time for two different values of coupling strength: η = 0 . 02 (dotted line) , and 0 . 08 (solid line). Parameters: ϵ$_{0}$ = 0 . 5 , ϵ$_{FR}$ = 0 , ϵ$_{FL}$ = 1 , $^{ℏ}$ω = 0 . 1 , Γ = 0 . 01. Units: all the parameters have same dimension as of $^{ℏ}$ω . In this work, we analyzed the time-dependent quantum transport of a resonant tunnel junction coupled to a nanomechanical oscillator by using the nonequilibrium Green’s function VII. SUMMARY 17 0 20 40 60 80 100 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Time Fano factor