Berlin 2005 – wissenschaftliches Programm

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A: Atomphysik

A 5: Atoms in External Fields

A 5.2: Fachvortrag

Samstag, 5. März 2005, 08:45–09:00, HU 3075

Novel efficient semiclassical quantization method for chaotic systems with pruned symbolic dynamics and application to the diamagnetic hydrogen atom — •J. Main — 1. Institut für Theoretische Physik, Universität Stuttgart, Germany

Semiclassical quantization methods have been successfully applied to the diamagnetic hydrogen atom at low energies and at very high energies, where the classical dynamics is fully hyperbolic and can be described by a complete symbolic dynamics. However, at energies around the field-free ionization limit, where the symbolic dynamics is strongly pruned, the atom has so far resisted all existing semiclassical techniques. We present a novel method based on high-resolution signal processing of the periodic orbit signal with amplitude constraints. A rather small set of ∼ 1500 periodic orbits, which have been obtained with a multi-shooting algorithm, is sufficient to calculate about 20 eigenvalues at energy E=0. The new method allows for the first time for the efficient quantization of a large variety of systems with pruned dynamics such as the hyperbola billiard, the closed three-disk billiard and the three-dimensional four-sphere system with touching spheres.