Volume 48, Number 3, November I 1999
|Page(s)||250 - 256|
|Published online||01 September 2002|
Semiclassical quantization by Padé approximant to periodic orbit sums
Institut für Theoretische Physik und Synergetik, Universität Stuttgart D-70550 Stuttgart, Germany
2 Department of Chemistry, University of Southern California Los Angeles, CA 90089, USA
Accepted: 7 September 1999
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Padé approximant to the periodic orbit sums. The Padé approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 03.65.Sq – Semiclassical theories and applications
© EDP Sciences, 1999
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