2002, Vol.5, No.4, pp.393-406
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.
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