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  • The level repulsion exponent of localized chaotic eigenstates as a function of the classical transport time scales in the stadium billiard [Elektronski vir]
    Batistić, Benjamin ; Lozej, Črt ; Robnik, Marko, 1954-
    We study the aspects of quantum localization in the stadium billiard, which is a classically chaotic ergodic system, but in the regime of slightly distorted circle billiard the diffusion in the ... momentum space is very slow. In quantum systems with discrete energy spectrum the Heisenberg time tH = 2 pi=delta E, where deltaE is the mean level spacing (inverse energy level density), is an important time scale. The classical transport time scale tT (diffusion time) in relation to the Heisenberg time scale tH (their ratio is the parameter alfa = tH=tT ) determines the degree of localization of the chaotic eigenstates, whose measure A is based on the information entropy. The localization of chaotic eigenstates is reflected also in the fractional power-law repulsion between the nearest energy levels in the sense that the probability density (level spacing distribution) to find successive levels on a distance S goes like alfa S beta for small S, where 0 equal or less 1, and beta = 1 corresponds to completely extended states. We show that the level repulsion exponent beta is a unique rational function of alfa, and A is a unique rational function of alfa. Beta goes from 0 to 1 when alfa goes from 0 to endless. Also, beta is a linear function of A, which is similar as in the quantum kicked rotator, but different from a mixed type billiard.
    Vir: Nonlinear phenomena in complex systems [Elektronski vir]. - ISSN 1817-2458 (Vol. 21, no. 3, 2018, str. 225-236)
    Vrsta gradiva - e-članek
    Leto - 2018
    Jezik - angleški
    COBISS.SI-ID - 95735297

    Povezava(-e):

    http://www.j-npcs.org/abstracts/vol2018no3.html

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