There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
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.