Chaotic tunneling: A remarkable manifestation of complex classical dynamics in non-integrable quantum phenomena

The tunneling phenomenon in chaotic systems is analyzed in terms of the complex semi-classical method in the time domain. In contrast to the tunneling paths in integrable systems, it is discovered that there exist a tremendous number of candidate complex branches (Laputa branches) which may contribute to the semi-classical propagator. The origin of a lot of characteristic structures observed in the tunneling tail in chaotic systems, which are completely absent in case of integrable systems, can fully be interpreted using such complex paths. In particular, we found a remarkable object forming chain-like structures (Laputa chains), which are hidden in the set of initial values displayed on the complex plane and they just generate a variety of structures in tunneling tails. The relationship between the tunneling tail and the structure of the Laputa chain is analyzed in detail. The candidate trajectories, however, contain non-physical non-contributing part as a manifestation of Stokes Phenomenon, and empirical rules on how to remove such non-contributing parts is also discussed. On the basis of the whole story constructed here, chaotic tunneling is proposed as a universal tunneling mechanism originating in the complicated structure of classical chaotic manifolds in the complex regime. Several questions arose in the present study, but not clarified yet, are also listed up in relation to the theories of complex semi-classical method and complex dynamical systems. Copyright (C) 1998 Elsevier Science B.V.