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  • Quantum localization of chaotic eigenstates and the level spacing distribution [elektronski vir]
    Batistić, Benjamin ; Robnik, Marko, 1954-
    The phenomenon of quantum localization in classically chaotic eigenstates is one of themain issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or ... even in general wave mechanics. In this work we propose two different localization measures characterizing the degree of quantum localization, and study their relation to another fundamental aspect of quantum chaos, namely the (energy) spectral statistics. Our approach and method is quite general, and we apply it to billiard systems. One of the signatures of the localization of chaotic eigenstates is a fractional power-law repulsion between the nearest energy levels in the sense that the probability density to find successive levels on a distance S goes like endles S beta for small S, where 0_beta_1, and beta = 1corresponds to completely extended states. We show that there is a clear functional relation between the exponent betta and the two different localization measures. One is based on the information entropy and the other one on the correlation properties of the Husimi functions. We show that the two definitions are surprisingly linearly equivalent. The approach is applied in the case of a mixed-type billiard system [M. Robnik, J. Phys. A: Math. Gen. 16, 3971 (1983)], in which the separation of regular and chaotic eigenstates is performed.
    Source: Physical review. E, Statistical, nonlinear and soft matter physics [Elektronski vir]. - ISSN 1550-2376 (Vol. 88, no. 5, 2013, str. 052913-1 - 052913-7)
    Type of material - e-article
    Publish date - 2013
    Language - english
    COBISS.SI-ID - 76225025
    DOI

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