Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2002-04-16
Nonlinear Sciences
Chaotic Dynamics
11 pages, 11 figures, submitted to Phys. Rev. E
Scientific paper
Classical chaotic systems with symbolic dynamics but strong pruning present a particular challenge for the application of semiclassical quantization methods. In the present study we show that the technique of periodic orbit quantization by harmonic inversion of trace formulae, which does not rely on the existence of a complete symbolic dynamics or other specific properties, lends itself ideally to calculating semiclassical eigenvalues from periodic orbit data even in strongly pruned systems. As the number of periodic orbits proliferates exponentially in chaotic systems, we apply the harmonic inversion technique to cross-correlated periodic orbit sums, which allows us to reduce the required number of orbits. The power of the method is demonstrated for the closed three-disk billiard as a prime example of a classically chaotic bound system with strong pruning.
Main Joerg
Weibert K.
Wunner Guenter
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