Complex trajectory description for chaotic tunneling

Chaotic tunneling occurring in the standard map, which is one of the most f amiliar paradigms in simple chaotic mappings, is analyzed in terms of compl ex semiclassical theory in the time domain. It is shown that the complex cl assical trajectories successfully describe the transition to the region whe re the real classical path cannot reach, in connection with our previous re sult (Physica D115 (1998), 234), the universality of the organizing rule to find out dominantly contributing complex paths is suggested. Several funda mental problems in the treatment of semiclassical theory in the complex dom ain are also discussed.