Real-Time Path Integral Methods, Quantum Master Equations, and Classical vs Quantum Memory

We investigate the use of accurate path integral methods, namely the quasi-adiabatic propagator path integral (QuAPI) and the quantum-classical path integral (QCPI), for generating the memory kernel entering generalized quantum master equations (GQME). Our calculations indicate that the length of the memory kernel in system-bath models is equal to the full length of time nonlocality encoded in the Feynman-Vernon influence functional and that the solution of the GQME with a QuAPI kernel is identical to that obtained through an iterative QuAPI calculation with the same memory length. Further, we show that the memory length in iterative QCPI calculations is always shorter than the GQME kernel memory length. This stems from the ability of the QCPI methodology to pretreat all memory effects of a classical nature (i.e., those associated with phonon absorption and stimulated emission), as well as some of the quantum memory contributions (arising from spontaneous phonon emission). Furthermore, trajectory-based iterative QCPI simulations can fully account for important structural/conformational changes that may occur on very long time scales and that cannot be captured via master equation treatments.