Classical and quantum rotation numbers of asymmetric top molecules

TL;DR

This paper investigates the relationship between classical and quantum rotation numbers in asymmetric top molecules, demonstrating convergence in the semi-classical limit and identifying spectral signatures of classical effects.

Contribution

It provides a numerical analysis of quantum-classical correspondence for asymmetric molecules and introduces a simple approximation near the separatrix.

Findings

Quantum rotation number converges to classical in semi-classical limit

Spectral signature of the classical tennis racket effect identified

Approximation of classical rotation number near the separatrix

Abstract

We study the classical and quantum rotation numbers of the free rotation of asymmetric top molecules. We show numerically that the quantum rotation number converges to its classical analog in the semi-classical limit. Different asymmetric molecules such as the water molecule are taken as illustrative example. A simple approximation of the classical rotation number is derived in a neighborhood of the separatrix connecting the two unstable fixed points of the system. Furthermore, a signature of the classical tennis racket effect in the spectrum of asymmetric molecules is identified.