Resonance-assisted tunneling in near-integrable systems - art. no. 064101

Dynamical tunneling between symmetry related invariant tori is studied in t he near-integrable regime. Using the kicked Harper model as an illustration , we show that the exponential decay of the wave functions in the classical ly forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation o f the splitting between quasidegenerate eigenvalues from the purely exponen tial decrease with 1/(h) over bar obtained for the integrable system. A sim ple semiclassical framework, which takes into account the effect of the res onance substructure on the invariant tori, allows one to quantitatively rep roduce the behavior of the eigenvalue splittings.