The twilight zone in the parametric evolution of eigenstates: beyond perturbation theory and semiclassics
J. A. Mendez-Bermudez, Tsampikos Kottos, Doron Cohen
Abstract
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. For the first time 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 co-exist. This is in contrast with the simple crossover from a Lorentzian to a semicircle line-shape which is found in random-matrix models.
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