Classical transients and the support of open quantum maps
Entity
UAM. Departamento de Física Teórica; UAM. Departamento de QuímicaDate
2013-01-17Citation
10.1103/PhysRevE.87.012909
Physical Review E 87.1 (2013): 012909
ISSN
1539-3755 (print); 1550-2376 (online)DOI
10.1103/PhysRevE.87.012909Funded by
This work was supported by the MICINN Spain under Contract No. MTM2009-14621, CEAL, and also CONICET, UBACyT, and ANPCyT (Argentina)Project
Gobierno de España. MTM2009-14621Editor's Version
http://dx.doi.org/10.1103/PhysRevE.87.012909Subjects
FísicaRights
© 2013 American Physical SocietyAbstract
The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support for quantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief that the classical repeller—the set of nonescaping orbits in the future and past evolution—is 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 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. We provide an interpretation of the results in order to have hints about them
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Google Scholar:Carlo, Gabriel G.
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Wisniacki, D. A.
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Ermann, Leonardo
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Benito, R. M.
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Borondo, Florentino
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