  Quantum path interferences or resonances in multilevel dissipative quantum
systems play an important and intriguing role in the transport processes of
nanoscale systems. Many previous minimalistic models used to describe the
quantum path interference driven by incoherent fields are based on the
approximations including the second order perturbation for the weak coupling
limit, the ad-hoc choices of two-time correlation functions and $\it{etc}$. On
the other hand, the similar model to study the non-adiabatic molecular
electronic excitation have been extensively developed and many efficient
quantum 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 scheme
to study the interactions of system-light and system-phonon simultaneously and
gain insight into and principles of the roles of quantum path interferences in
the realistic molecular systems. I discuss how to derive the time-dependent
stochastic Schr$\ddot{o}$dinger equation from the Ehrenfest scheme as a
foundation to discuss the detailed balance for the weak coupling limit and
therefore the quantum correction in the Ehrenfest scheme. Different from the
master equation technique, the Ehrenfest scheme doesn't need any specific
assumptions about spectral densities and two time correlation functions. With
simple open two-level and three-level quantum systems, I show the effect of the
quantum path interference on the steady state populations. Currently I only
focus on the role of the phonon thermal reservoir. The electromagnetic field
(solar light) will be modeled as a thermal reservoir and discussed in detail in
the future paper.
