Spatial Correlations in Chaotic Eigenfunctions

Abstract

At short distances, energy eigenfunctions of chaotic systems have spatial correlations that are well described by assuming a microcanonical density in phase space for the corresponding Wigner function. However, this is not correct on large scales. The correct correlation function is in turn needed to get the correct formula for the root-mean-square value of the off-diagonal matrix elements of simple observables, and for the fluctuations in the diagonal elements.