Europhys. Lett, 48 (3), pp. 250-256 (1999)
Semiclassical quantization by Padé approximant to periodic orbit sums
J. Main 1, P. A. Dando 2, D. Belkic 2 and H. S. Taylor 2
1 Institut für Theoretische Physik und Synergetik,
D-70550 Stuttgart, Germany
2 Department of Chemistry, University of Southern California
Los Angeles, CA 90089, USA
(received 27 May 1999; accepted in final form 7 September 1999)
PACS. 05.45-a - Nonlinear dynamics and nonlinear dynamical systems.
PACS. 03.65Sq - Semiclassical theories and applications.
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.
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