Open quantum–classical systems: A hybrid MASH master equation

We propose a method that combines the quantum–classical mapping approach to surface hopping with the dissipative quantum dynamics of the Lindblad master equation. Like conventional surface-hopping methods, our approach is based on classical trajectories coupled to the dynamics of a quantum subsystem. However, instead of evolving the subsystem wavefunction according to the time-dependent Schrödinger equation, we use stochastic quantum trajectories derived from secular Redfield theory. This approach enables the simulation of open quantum systems coupled simultaneously to Markovian quantum baths and anharmonic, non-Markovian classical degrees of freedom. Applications to the spin–boson model and to the cavity-enhanced fluorescence of an electronically nonadiabatic molecule show excellent agreement with fully quantum-mechanical benchmarks.