Perturbations and Chaos in quantum maps

DIEGO A. WISNIACKI; DARIO BULLO

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2012 vol. 86 p. 26206 - 26206

1539-3755

The local density of states (LDOS) is a distribution that characterizes the effects of perturbations on quantum systems. Recently, a semiclassical theory was proposed for the LDOS of chaotic billiards and maps. This theory predicts that the LDOS is a Breit-Wigner distribution independent of the perturbation strength and also gives a semiclassical expression for the LDOS width. Here, we test the validity of such an approximation in quantum maps by varying the degree of chaoticity, the region in phase space where the perturbation is applied, and the intensity of the perturbation. We show that for highly chaotic maps or strong perturbations the semiclassical theory of the LDOS is accurate to describe the quantum distribution. Moreover, the width of the LDOS is also well represented for its semiclassical expression in the case of mixed classical dynamics.