Classical transients and the support of open quantum maps

GABRIEL G. CARLO; DIEGO WISNIACKI; LEONARDO ERMANN; ROSA M. BENITO; FLORENTINO BORONDO

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2013 vol. 87 p. 12909 - 12916

1539-3755

The basic ingredients in a semiclassical theory are the classical invariant objects serving as a support forquantization. Recent studies, mainly obtained on quantum maps, have led to the commonly accepted belief thatthe classical repeller—the set of nonescaping orbits in the future and past evolution—is the object that suitablyplays this role in open scattering systems. In this paper we present numerical evidence warning that this maynot 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 asymptoticproperties but differ in their short-time behavior. We have found that although the eigenvalue distribution of theevolution operator of these maps follows the fractal Weyl law prediction, the theory of short periodic orbits foropen maps fails to describe the resonance eigenfunctions of some of them. This is a strong indication that newelements must be included in the semiclassical description of open quantum systems. We provide an interpretationof the results in order to have hints about them.