Statistical properties of energy levels in quantum reaction dynamics: a case study

Abstract

An account is presented of recent approaches to the characterization of the statistical properties of the energy level sequences of interest in quantum reaction dynamics. The case study of the quantum eigenvalues of the reactive process F+ H₂→ HF+ H as a function of the hyperradius (a measure of the total inertia of the three-body system) is illustrated. Previous work is extended by examining different angular momentum projection values for two recently proposed potential energy surfaces. We study spectral properties such as the standard deviation σ of the level spacings and the shape of the nearest-neighbour spacing distribution (NNSD), evaluating the q parameters of the Brody and Berry–Robnik distributions, which are alternative interpolations between the Poisson and the Wigner distributions. We also apply statistical tools, such as the

test (which is analogous to the Δ₃(L) of Dyson and Mehta) and the correlation coefficient C(r). This analysis, which is typical of current investigations on the topic of ‘quantum chaos’, gives insight into the nature of the reactive event and may be useful for the development of statistical theories in molecular dynamics.