Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2010-11-03
Phys. Rev. E 82, 066207 (2010)
Nonlinear Sciences
Chaotic Dynamics
10 pages, 9 figures
Scientific paper
10.1103/PhysRevE.82.066207
The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters. 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. The periodic orbit bunches can significantly improve the efficiency of semiclassical quantization methods for classically chaotic systems, which suffer from the exponential proliferation of orbits. For the diamagnetic hydrogen atom the use of one or few representatives of a periodic orbit bunch in Gutzwiller's trace formula allows for the computation of semiclassical spectra with a classical data set reduced by up to a factor of 20.
Gehrke Jan
Main Jörg
Wunner Günter
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