Geometric Effects on Tunneling in Driven Quantum Systems

We review quantum tunneling provoked by external field driving, focusing on the role of geometric effects. The discussion begins with an overview of tunneling phenomena, including the Landau-Zener model and the Schwinger effect, both of which are essential frameworks to describe the generation of elementary excitation of the system. We also refer to the relation between the modern theory of polarization and the geometry of the system, and introduce the shift vector via adiabatic perturbation theory. Then we introduce the twisted Landau-Zener model and shown how the shift vector modulates tunneling probability, followed by several illustrative applications of this model. We also explain the Keldysh crossover, which is the crossover from a quantum tunneling regime to photon absorption regime in driven systems.