Partition-free approach to open quantum systems in harmonic   environments: an exact stochastic Liouville equation
  We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the Extended Stochastic Liouville-von Neumann equation. Our approach generalises previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed. 
G.M.G. McCaul, C.D. Lorenz and L. Kantorovich
quant-ph cond-mat.stat-mech