Complex Classical Trajectories and Chaotic Tunneling

Tunneling phenomena in the presence of chaos are investigated. Several remarkable features, which form a sharp contrast to the tunneling in the integrable system, can be well understood in terms of the semiclassical theory including complex classical trajectories. In particular, it is found that the dominant contribution to the tunneling regime comes from many complex branches which are not connected with any real manifolds and are linked at caustics to form the bifurcation chains. Chaotic tunneling is proposed as a new class of tunneling phenomena which originate from the complicated nature of the complex dynamical system.