Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2001-09-04
J. Phys. A 34 (2001) 7381-7391
Nonlinear Sciences
Chaotic Dynamics
Revtex, 13 pages, 1 postscript figure
Scientific paper
10.1088/0305-4470/34/36/317
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.
Li Baowen
Rouben Daniel C.
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