Dynamics of quantum dissipation systems interacting with Fermion and   Boson grand canonical bath ensembles: Hierarchical equations of motion   approach
  A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed, on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovin bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the Fermion or Boson bath interaction are found to be of the same path-integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism are different, due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed. 
Jinshuang Jin, Sven Welack, JunYan Luo, Xin-Qi Li, Ping Cui, Rui-Xue   Xu, and YiJing Yan