Statistical properties of eigenstates beyond random matrix theory

摘要

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.