Parametric evolution of eigenstates: beyond perturbation theory and semiclassics.
Considering a quantized chaotic system, we analyze the evolution of its eigenstates as a result of varying a control parameter. As the induced perturbation becomes larger, there is a crossover from a perturbative to a non-perturbative regime, which is reflected in the structural changes of the local density of states. The full scenario is explored for a physical system: an Aharonov-Bohm cylindrical billiard. As we vary the magnetic flux, we discover an intermediate twilight regime where perturbative and semiclassical features coexist. This is in contrast with the simple crossover from a Lorentzian to a semicircle line shape which is found in random-matrix models.
Méndez-Bermúdez
J A
JA
Max-Planck-Institute for Dynamics and Self-Organnization, 37073 Göttingen, Germany.
Kottos
Tsampikos
T
Cohen
Doron
D