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The formation of the plateau spectrum is a manifestation of the classical unstable manifold in multi-dimensional barrier tunneling, for which contributing tunneling trajectories are guided by the stable and unstable manifolds in the complex domain. In this paper, we numerically confirm that the plateau spectrum is generally observed for a wide class of multi-dimensional barrier potentials. The results of complex semiclassical analysis are also discussed.

Multi-mode lasing in stadium-shaped cavities which are rigorously known to be fully chaotic is investigated both theoretically and experimentally. By a nonlinear dynamical model, it is shown that there exist multi-attractors of limit cycles and chaos corresponding to the final lasing states for large microstadiums. We also show that the envelopes of the far field patterns of the actual microstadium laser diodes are excellently approximated by fully chaotic ray-dynamics.

Recent studies on complex dynamical systems in more than one dimension have revealed that even if the real phase space is a mixture of KAM tori and chaotic seas there exists a unique ergodic measure in the complex phase space which is (weakly) hyperbolic and gives maximal entropy of the dynamics. We present several pieces of numerical evidence and speculations on the existence of rotational domains in the complex space, implying that the measure thus obtained satisfies desired properties of the support of semiclassical wavefunctions in the mixed phase space.

Chaotic tunneling occurring in the standard map, which is one of the most familiar paradigms in simple chaotic mappings, is analyzed in terms of complex semiclassical theory in the time domain. It is shown that the complex classical trajectories successfully describe the transition to the region where the real classical path cannot reach. In connection with our previous result (Physica D115 (1998), 234), the universality of the organizing rule to find out dominantly contributing complex paths is suggested. Several fundamental problems in the treatment of semiclassical theory in the complex domain are also discussed.