Classical invariants and the quantization of chaotic systems

D. A. WISNIACKI, E. VERGINI, R. M. BENITO, AND F. BORONDO

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Año: 2004 vol. 70 p. 352021 - 352024

1063-651X

Due to their exponential proliferation, long periodic orbits constitute a serious drawback in Gutzwiller’s theory of chaotic systems. Therefore, it would be desirable that other classical invariants, not suffering from the same problem, could be used in alternative semiclassical quantization schemes. In this Rapid Communication, we demonstrate how a suitable dynamical analysis of chaotic quantum spectra unveils the role played, in this respect, by classical invariant areas related to the stable and unstable manifolds of short periodic orbits.