Chaos attracts tunneling trajectories: A universal mechanism of chaotic tunnelingA. Shudo1, Y. Ishii2 and K. S. Ikeda3
1 Department of Physics, Tokyo Metropolitan University - Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan
2 Department of Mathematics, Kyushu University - Ropponmatsu, Fukuoka 810-8560, Japan
3 Department of Physics, Ritsumeikan University - Noji-higashi 1-1-1, Kusatsu 525-8577, Japan
received 31 October 2007; accepted in final form 8 January 2008; published March 2008
published online 11 February 2008
It is shown that stable and unstable manifolds in the complex plane control dynamical tunneling in mixed systems. Some hypotheses based upon numerical observations combined with recent results in the theory of complex dynamical systems (Bedford and Smillie 1991, 1992) reveal that the stable manifolds in complex space are densely distributed in the set of tunneling orbits which asymptotically contribute to the semiclassical propagator. It is indeed verified that the tunneling amplitude out of the KAM region is well reproduced by the orbits attracted by unstable periodic orbits in the real phase space.
05.45.Mt - Quantum chaos: semiclassical methods.
03.65.Sq - Semiclassical theories and applications.
05.45.-a - Nonlinear dynamics and chaos.
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