Scaling laws and correlation lengths of quantum and classical ergodic states

Abstract

The semiclassical analog of the spatial quantum wavefunction correlation is shown to be identical, over short ranges, to its quantum counterpart for the vast majority of high-lying stadium eigenstates. Also, the semiclassical and pure quantum correlation lengths are shown to scale as the local de Bfoglie wavelength, a feature related to quantum ergodicity. Cross correlation and the time evolution of correlation lengths for non-stationary quantum states are then examined and the latter is shown to be a near constant of the motion for chaotic wavepackets. This characteristic may relate to features of quantum mixing.