Characterization of random features of chaotic eigenfunctions in unperturbed basis

Abstract

In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's conjecture, it is shown that the components in classically allowed regions can be regarded as Gaussian random numbers in certain sense, when appropriately rescaled with respect to the average shape of the eigenfunctions. This suggests that, when a perturbed system changes from integrable to chaotic, deviation of the distribution of rescaled components in classically allowed regions from the Gaussian distribution may be employed as a measure for the ``distance'' to quantum chaos. Numerical simulations performed in the LMG model and the Dicke model show that this deviation coincides with the deviation of the nearest-level-spacing distribution from the prediction of random-matrix theory. Similar numerical results are also obtained in two models without classical counterpart.

arXiv comment11 pages, 13 figures

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Cited by in corpus (5)

• Average entanglement entropy of midspectrum eigenstates of quantum-chaotic interacting Hamiltonians
• Chaos and Thermalization in the Spin-Boson Dicke Model
• Convergent perturbation expansion of energy eigenfunctions on unperturbed basis states in classically-forbidden regions
• Integral Fluctuation Theorem for Microcanonical and Pure States
• Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems