1. Characterization of random features of chaotic eigenfunctions in unperturbed basis
- Author
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Jiaozi Wang and Wenge Wang
- Subjects
Physics ,Integrable system ,Statistical Mechanics (cond-mat.stat-mech) ,Gaussian ,Chaotic ,Semiclassical physics ,FOS: Physical sciences ,Nonlinear Sciences - Chaotic Dynamics ,01 natural sciences ,Measure (mathematics) ,Quantum chaos ,010305 fluids & plasmas ,symbols.namesake ,Distribution (mathematics) ,0103 physical sciences ,symbols ,Statistical physics ,Chaotic Dynamics (nlin.CD) ,010306 general physics ,Quantum ,Condensed Matter - Statistical Mechanics - 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., Comment: 11 pages, 13 figures
- Published
- 2023
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