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Title: Correlations of chaotic eigenfunctions: A semiclassical analysis
Authors: Li, B. 
Rouben, D.C.
Issue Date: 14-Sep-2001
Source: Li, B., Rouben, D.C. (2001-09-14). Correlations of chaotic eigenfunctions: A semiclassical analysis. Journal of Physics A: Mathematical and General 34 (36) : 7381-7391. ScholarBank@NUS Repository.
Abstract: We derive a semiclassical expression for an energy-smoothed autocorrelation function defined on a group of eigenstates of the Schrödinger equation. The system we consider 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.
Source Title: Journal of Physics A: Mathematical and General
ISSN: 03054470
DOI: 10.1088/0305-4470/34/36/317
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