Semiclassical wavefunctions of nonintegrable systems and localization on periodic orbits

Abstract

We review semiclassical approximations for wavefunctions, including the EBK approximation for integrable systems and the recent work of Bogomolny and Berry for nonintegrable systems, stemming from the periodic orbit theory of Gutzwiller and Balian and Block. In particular we focus on the localization around periodic orbits (scarring) first appreciated by Heller, and the description of this scarring in both coordinate and phase space. We examine individual wavefunctions of a schematic shell model in phase space and find that few are ergodic. We also find that the degree of localization depends both on the degree of chaos in the classical limit and on the nearness of the eigenvalue to an energy that quantizes the scarring periodic orbit.