Direct dynamical tunneling in systems with a mixed phase space

Tunneling in 1D describes the effect that quantum particles can penetrate a classically insurmountable potential energy barrier. The extension to classically forbidden transitions in phase space generalizes the tunneling concept. A typical 1D Hamiltonian system has a mixed phase space. It contains regions of regular and chaotic dynamics, the so-called regular islands and the chaotic sea. These different phase space components are classically separated by dynamically generated barriers. Quantum mechanically they are, however, connected by dynamical tunneling. We perform a semiclassical quantization of almost resonance-free regular islands and transporting island chains of quantum maps. This yields so-called quasimodes, which are used for the investigation of direct dynamical tunneling from an almost resonance-free regular island to the chaotic sea. We derive a formula which allows for the determination of dynamical tunneling rates. Good agreement between this analytical prediction and numerical results is found over several orders of magnitude for two example systems.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Technische Universität Dresden

Year

2007

Author dc:creator

• Schilling, Lars

Contributors dc:contributor

• Ketzmerick, Roland
• Rost, Jan-Michael
• Tomsovic, Steven L.

• Dynamical tunneling
• Semiclassical quantization
• Mixed phase space
• Dynamisches Tunneln
• Semiklassische Quantisierung
• Gemischter Phasenraum