The twilight zone in the parametric evolution of eigenstates: beyond perturbation theory and semiclassics

TL;DR

This paper investigates how eigenstates of a chaotic quantum system evolve with changing parameters, revealing a complex intermediate regime where perturbative and semiclassical features coexist, beyond traditional perturbation theory and semiclassical analysis.

Contribution

It provides the first detailed exploration of the full evolution scenario in a physical system, highlighting the twilight regime in eigenstate evolution.

Findings

Identification of a twilight regime with coexisting features

Contrast with random-matrix model predictions

Observation of structural changes in local density of states

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.