Correspondence between classical and quantum resonances

TL;DR

This paper explores how classical bifurcations in molecular systems manifest as quantum resonances, establishing a correspondence through eigenenergy analysis and developing a semiclassical theory.

Contribution

It introduces a method to identify quantum resonances corresponding to classical bifurcations using eigenenergy correlation diagrams and provides analytical semiclassical expressions.

Findings

Series of avoided crossings correspond to classical resonances.

Extrapolation to  reveals classical-quantum energy correspondence.

Develops a semiclassical theory for analytical insights.

Abstract

Bifurcations take place in molecular Hamiltonian nonlinear systems as the excitation energy increases, this leading to the appearance of different classical resonances. In this paper, we study the quantum manifestations of these classical resonances in the isomerizing system CN-Li$\leftrightarrows$Li-CN. By using a correlation diagram of eigenenergies versus Planck constant, we show the existence of different series of avoided crossings, leading to the corresponding series of quantum resonances, which represent the quantum manifestations of the classical resonances. Moreover, the extrapolation of these series to $\hbar=0$ unveils the correspondence between the bifurcation energy of classical resonances and the energy of the series of quantum resonances in the semiclassical limit $\hbar\to0$. Additionally, in order to obtain analytical expressions for our results, a semiclassical theory is developed.