Periodic Orbit Quantization of the Closed Three-disk Billiard as an Example of a Chaotic System with Strong Pruning
نویسندگان
چکیده
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, and the limitations, of the method in its present form are demonstrated for the closed three-disk billiard as a prime example of a classically chaotic bound system with strong pruning.
منابع مشابه
Periodic orbit quantization of chaotic systems with strong pruning
The three-disk system, which for many years has served as a paradigm for the usefulness of cycle expansion methods, represents an extremely hard problem to semiclassical quantization when the disks are moved closer and closer together, since (1) pruning of orbits sets in, rendering the symbolic code incomplete, and (2) the number of orbits necessary to obtain accurate semiclassical eigenvalues ...
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