Classical transients and the support of open quantum maps

Abstract

The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for the quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that it is the classical repeller -- the set of non escaping orbits in the future and past evolution -- the object that suitably plays this role in open scattering systems. In this paper we present numerical evidence warning that this may not always be the case. For this purpose we study recently introduced families of tribaker maps [L. Ermann, G.G. Carlo, J.M. Pedrosa, and M. Saraceno, Phys. Rev. E {\bf 85}, 066204 (2012)], which share the same asymptotic properties but differ in their short time behavior. We have found that although the eigenvalue distribution of the evolution operator of these maps follows the fractal Weyl law prediction, the theory of short periodic orbits for open maps fails to describe the resonance eigenfunctions of some of them. This is a strong indication that new elements must be included in the semiclassical description of open quantum systems.

7 pages, 9 figures

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Cited by in corpus (8)

• Resonances in open quantum maps
• Resonance eigenfunction hypothesis for chaotic systems
• Short periodic orbits theory for partially open quantum maps
• Lagrangian descriptors for open maps
• The role of short periodic orbits in quantum maps with continuous openings
• Semiclassical theory of chaotic quantum resonances
• Resonance states of the three-disk scattering system
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization