Statistical properties of chaotic wavefunctions in two and more dimensions

Abstract

Starting with Berry's hypothesis for fixed energy waves in a classically chaotic system, and casting it in a Green function form, we derive wavefunction correlations and density matrices for few or many particles. Universal features of fixed energy (microcanonical) random wavefunction correlation functions appear which reflect the emergence of the canonical ensemble as N↦∞. This arises through a little known asymptotic limit of Bessel functions. The Berry random wave hypothesis in many dimensions may be viewed as an alternative approach to quantum statistical mechanics, when extended to include constraints and potentials.