Resonance-assisted tunneling in near-integrable systems

Details Resonance-assisted tunneling in near-integrable systems Resonance-assisted tunneling in near-integrable systems

2001-04-04

arxiv.org/abs/nlin/0104010v2

Phys. Rev. Lett. 87, 064101 (2001)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 2 figures, gzipped tar file, to appear in Phys. Rev. Lett, text slightly condensed compared to first version

Scientific paper

10.1103/PhysRevLett.87.064101

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasi-degenerate eigenvalues from the purely exponential decrease with 1 / hbar obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the KAM tori, allows to quantitatively reproduce the behavior of the eigenvalue splittings.

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