# Parametric evolution of eigenstates: Beyond perturbation theory and semiclassics Academic Article

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### 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 {\em 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 {\em simple} crossover from a Lorentzian to a semicircle line-shape which is found in random-matrix models.

### publication date

• January 1, 2005