Statistical Properties of Chaotic Quantum Dynamics

Abstract

<p> The statistical properties ofT-shaped Ar3 energy eigenvalues and eigenfunctions are investigated and are used to characterize the system as quantum chaotic. The statistical properties of quantum chaos suggest a statistical theory of quantum dynamics. This statistical quantum dynamics is proposed as an alternative to full scale numerical simulation of quantum dynamics which requires the manipulation of very large matrices. Sparse matrix technology has made the latter computations more tractable; however, a simple alternative based on statistical approximations is still very desirable. The newly proposed statistical theory is tested against sparsematrix based numerical simulation of the T-shaped Ar3 inversion dynamics. The unsuccessful results are rationalized in terms of correlations between eigenfunctions not represented in the statistical theory. </p>