Use of harmonic inversion techniques in the periodic orbit quantization of integrable systems |
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Authors: | K Weibert J Main G Wunner |
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Institution: | 1. Institut für Theoretische Physik und Synergetik, Universit?t Stuttgart, 70550, Stuttgart, Germany
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Abstract: | Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit
orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the periodic
orbit sum and the uncertainty principle of the usual Fourier analysis, thus yielding results of high resolution and high precision.
Based on the close analogy between periodic orbit trace formulae for regular and chaotic systems the technique is generalized
in this paper for the semiclassical quantization of integrable systems. Thus, harmonic inversion is shown to be a universal
tool which can be applied to a wide range of physical systems. The method is further generalized in two directions: firstly,
the periodic orbit quantization will be extended to include higher order corrections to the periodic orbit sum. Secondly, the use of cross-correlated periodic orbit sums allows us to significantly
reduce the required number of orbits for semiclassical quantization, i.e., to improve the efficiency of the semiclassical method. As a representative of regular systems, we choose the circle billiard,
whose periodic orbits and quantum eigenvalues can easily be obtained.
Received 24 February 2000 and Received in final form 22 May 2000 |
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Keywords: | PACS 03 65 Sq Semiclassical theories and applications |
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