Complex-domain semiclassical theory: Application to time-dependent barriertunneling problems

Semiclassical theory based upon complexified classical mechanics is develop ed for periodically time-dependent scattering systems, which are minimal mo dels of multi-dimensional systems. Semiclassical expression of the wave-mat rix is derived, which is represented as the sum of the contributions from c lassical trajectories, where all the dynamical variables as well as the tim e are extended to the complex-domain. The semiclassical expression is exami ned by a periodically perturbed 1D barrier system and an excellent agreemen t with the fully quantum result is confirmed. In a stronger perturbation re gime, the tunneling component of the wave-matrix exhibits ar remarkable int erference fringes, which is clarified by the semiclassical theory as an int erference among multiple complex tunneling trajectories. It turns out that such a peculiar behavior is the manifestation of an intrinsic multi-dimensi onal effect closely related to a singular movement of singularities possess ed by the complex classical trajectories.