Hamburg 2009 – scientific programme

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A: Fachverband Atomphysik

A 17: Atomic Systems in External Fields III

A 17.5: Talk

Wednesday, March 4, 2009, 15:15–15:30, VMP 6 HS-C

Semiclassical quantization of the diamagnetic hydrogen atom with near action-degenerate periodic orbit bunches — •Jan Gehrke, Jörg Main, and Günter Wunner — 1. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart

Gutzwiller’s trace formula for the semiclassical quantization of classically chaotic systems suffers from the exponential proliferation of periodic orbits, and it is an important question whether semiclassical eigenstates can be obtained with reduced classical input data. It has been shown [1] that the periodic orbits of chaotic systems appear in "bunches". Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters. We show the existence of periodic orbit bunches for the diamagnetic Kepler problem and demonstrate that the orbits can be grouped already on the level of the symbolic dynamics by application of appropriate reconnection rules to the symbolic code in the ternary alphabet. This allows for the use of one or few representatives of a periodic orbit bunch in Gutzwiller’s trace formula. For the diamagnetic hydrogen atom semiclassical spectra obtained with the complete set of periodic orbits and the, up to a factor of 20 reduced, set of bunch representatives agree very well.

[1] Sebastian Müller, Stefan Heusler, Petr Braun, Fritz Haake, and Alexander Altland, Phys. Rev. E 72, 046207 (2005).