Constructing quantum dynamics from mixed quantum-classical descriptions

Abstract

Abstract The influence of quantum bath effects on the dynamics of a quantum two-level system linearly coupled to a harmonic bath is studied when the coupling is both diagonal and off-diagonal. It is shown that the pure dephasing kernel and the non-adiabatic quantum transition rate between Born–Oppenheimer states of the subsystem can be decomposed into a contribution from thermally excited bath modes plus a zero point energy contribution. This quantum rate can be modewise factorized exactly into a product of a mixed quantum subsystem-classical bath transition rate and a quantum correction factor. This factor determines dynamics of quantum bath correlations. Quantum bath corrections to both the transition rate and the pure dephasing kernel are shown to be readily evaluated via a mixed quantum-classical simulation. Hence, quantum dynamics can be recovered from a mixed quantum-classical counterpart by incorporating the missing quantum bath corrections. Within a mixed quantum-classical framework, a simple approach for evaluating quantum bath corrections in calculation of the non-adiabatic transition rate is presented.