Statistical properties of eigenstates beyond random matrix theory

Abstract

A Green's function approach is developed for the purpose of determining wavefunction correlations in chaotic systems. We replace averaging over ‘random’ wavefunctions adapted to fit boundary conditions, or averaging over energy, by an ensemble of boundary conditions. We show the equivalence of the various approaches in cases where they all work, but argue that boundary condition ensembles are most general and suggestive of generalization to other contexts, including smooth boundaries, collisions, and many body systems.

Keywords:

• Random matrix theory
• Eigenstates
• Statistical properties

Acknowledgements

This paper is in honor of Bob Harris' contributions to chemical physics, which have raised many new and fundamental questions, and have helped to keep heads above the rising tide of purely numerical studies. This work was supported by a grant from the National Science Foundation, NSF CHE-0073544.