Correlations of chaotic eigenfunctions: a semiclassical analysis

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 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.

Revtex, 13 pages, 1 postscript figure

Cited by in corpus (5)

• Autocorrelation function of eigenstates in chaotic and mixed systems
• Semiclassical spatial correlations in chaotic wave functions
• Phase-space correlations of chaotic eigenstates
• Orbit bifurcations and wavefunction autocorrelations
• Transmission phase of a quantum dot and statistical fluctuations of partial-width amplitudes