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      Correlations of chaotic eigenfunctions: a semiclassical analysis

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          Abstract

          We derive a semiclassical expression for an energy smoothed autocorrelation function defined on a group of eigenstates of the Schr\"odinger equation. The system we considered is an energy-conserved Hamiltonian system possessing time-invariant symmetry. The energy smoothed autocorrelation function is expressed as a sum of three terms. The first one is analogous to Berry's conjecture, which is a Bessel function of the zeroth order. The second and the third terms are trace formulae made from special trajectories. The second term is found to be direction dependent in the case of spacing averaging, which agrees qualitatively with previous numerical observations in high-lying eigenstates of a chaotic billiard.

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          Journal
          2001-09-03
          Article
          10.1088/0305-4470/34/36/317
          nlin/0109005
          15dd8eb6-a53b-414c-9834-549b041e0ed1
          History
          Custom metadata
          J. Phys. A 34 (2001) 7381-7391
          Revtex, 13 pages, 1 postscript figure
          nlin.CD cond-mat

          Nonlinear & Complex systems
          Nonlinear & Complex systems

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