  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.
