Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2011-05-26
Nonlinear Sciences
Chaotic Dynamics
41 pages, 12 figures, preprint version of Chapter 8 of the book "Dynamical Tunneling - Theory and Experiment" edited by S. Kes
Scientific paper
We present a comprehensive theory of resonance-assisted tunneling in quantum systems that exhibit a mixed regular-chaotic classical phase space structure. After general considerations, we specifically focus on quantum systems with one degree of freedom that are subject to a periodic sequence of kicks or to a periodic driving. Tunneling takes place between energetically degenerate quasimodes that are localized on symmetric regular islands within the stroboscopic Poincare surface of section. In contrast to previous theoretical descriptions of resonance-assisted tunneling, we derive a more precise expression for the effective coupling matrix elements that induce the resonance-assisted tunneling process, and we take into account the influence of partial barriers within the chaotic part of the phase space. Comparison with numerically computed level splittings of eigenphases within the quantum kicked rotor shows very good agreement.
Mouchet Amaury
Schlagheck Peter
Ullmo Denis
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