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Quantum path interferences or resonances in multilevel dissipative quantumsystems play an important and intriguing role in the transport processes ofnanoscale systems. Many previous minimalistic models used to describe thequantum path interference driven by incoherent fields are based on theapproximations including the second order perturbation for the weak couplinglimit, the ad-hoc choices of two-time correlation functions and $\it{etc}$. Onthe other hand, the similar model to study the non-adiabatic molecularelectronic excitation have been extensively developed and many efficientquantum molecular dynamics simulation schemes, such as the Ehrenfest scheme,have been proposed.  In this paper, I aim to propose an unified model, extend the Ehrenfest schemeto study the interactions of system-light and system-phonon simultaneously andgain insight into and principles of the roles of quantum path interferences inthe realistic molecular systems. I discuss how to derive the time-dependentstochastic Schr$\ddot{o}$dinger equation from the Ehrenfest scheme as afoundation to discuss the detailed balance for the weak coupling limit andtherefore the quantum correction in the Ehrenfest scheme. Different from themaster equation technique, the Ehrenfest scheme doesn't need any specificassumptions about spectral densities and two time correlation functions. Withsimple open two-level and three-level quantum systems, I show the effect of thequantum path interference on the steady state populations. Currently I onlyfocus on the role of the phonon thermal reservoir. The electromagnetic field(solar light) will be modeled as a thermal reservoir and discussed in detail inthe future paper.

Quantum Path Interference through Incoherent Motions in Multilevel Quantum Systems