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  • Chaos and energy level statistics
    Robnik, Marko, 1954-
    We present improved numerical evidence for the applicability of the Random Matrix Theories, i.e. GOE or GUE characteristics, to the energy level statistics of those quantum systems whose Hamiltonian ... dynamics (with a small number of freedom) exhibits ergodicity (i.e. classical chaos). We also address the universality class of the Poissonian statistics in classically integrable quantal Hamiltonians, and raise the question of the adequacy and accuracy of the semiclassical approximations (such as the torus quantization and the Gutzwiller theory). Further, we show the numerical results on the level statistics for the generic (KAM) systems in the transition region between integrability and chaos. Our statistically highly significant data clearly show the existence of the fractional power law level repulsion at small spacings, and globally the adequacy of the Brody and Brody-like (such as Izrailev) distributions. At large spacings the Berry-Robnik approach is seen to be adequate. We discuss possible theoretical approaches such as the sparsed banded random matrix ensembles (SBRME), and the Dyson-Pechukas-Yukawa approach. Finally, we discuss the spectral statistics of the so-called composite systems, i.e. classically ergodic systems having the finite-time structure in the classical phase space due to the finite transport times, which are manifested in the near simiclassical limit, whereas the late semiclassical limit obeys the GOE\GUE statistics
    Vir: Taxe kai chaos. Tomos 4, Polyplokotetas kai chaotikes dynamikes me grammikõn systematõn (Str. 59-85)
    Vrsta gradiva - prispevek na konferenci
    Leto - 1998
    Jezik - angleški
    COBISS.SI-ID - 9376601

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