Floquet nonadiabatic dynamics in open quantum systems

The Born-Oppenheimer (BO) approximation has shaped our understanding on molecular dynamics microscopically in many physical and chemical systems. However, there are many cases that we must go beyond the BO approximation, particularly when strong light-matter interactions are considered. Floquet theory offers a powerful tool to treat time-periodic quantum systems. In this overview, we briefly review recent developments on Floquet nonadiabatic dynamics, with a special focus on open quantum systems. We first present the general Floquet Liouville von-Neumann (LvN) equation. We then show how to connect Floquet operators to real time observables. We proceed to outline the derivation of the Floquet quantum master equation in treating the dynamics under periodic driving in open quantum systems. We further present the Floquet mixed quantum classical Liouville equation (QCLE) to deal with coupled electron-nuclear dynamics. Finally, we embed FQCLE into a classical master equation (CME) to deal with Floquet nonadiabatic dynamics in open quantum systems. The formulations are general platforms for developing trajectory based dynamical approaches. As an example, we show how Floquet QCLE and Floquet CME can be implemented into a Langevin dynamics with Lorentz force and surface hopping algorithms.