Reduced density matrix hybrid approach: An efficient and accurate method   for adiabatic and non-adiabatic quantum dynamics
  We present a new approach to calculate real-time quantum dynamics in complex systems. The formalism is based on the partitioning of a system's environment into "core" and "reservoir" modes, with the former to be treated quantum mechanically and the latter classically. The presented method only requires the calculation of the system's reduced density matrix averaged over the quantum core degrees of freedom which is then coupled to a classically evolved reservoir to treat the remaining modes. We demonstrate our approach by applying it to the spin-boson problem using the noninteracting blip approximation to treat the system and core, and Ehrenfest dynamics to treat the reservoir. The resulting hybrid methodology is accurate for both fast and slow baths, since it naturally reduces to its composite methods in their respective regimes of validity. In addition, our combined method is shown to yield good results in intermediate regimes where neither approximation alone is accurate and to perform equally well for both strong and weak system-bath coupling. Our approach therefore provides an accurate and efficient methodology for calculating quantum dynamics in complex systems. 
Timothy C. Berkelbach, David R. Reichman, and Thomas E. Markland
cond-mat.stat-mech physics.chem-ph quant-ph