Signatures of the classical transition state in atomic quantum spectra

TL;DR

This paper demonstrates a clear link between classical transition states and quantum spectra in the hydrogen atom under external fields, revealing spectral signatures of classical phase space structures.

Contribution

It provides the first quantum calculations showing direct signatures of classical transition states in atomic spectra under crossed fields.

Findings

Spectral features correspond to classical saddle points.

Structures in spectra match classical energy levels near the saddle.

Evidence of classical transition states in quantum spectra.

Abstract

We perform quantum mechanically exact calculations of resonances in the spectrum of the hydrogen atom in crossed external fields and establish a close connection between the classical transition state in phase space and features in the quantum spectrum. By varying the external field strengths, structures are revealed which are surprisingly similar to the quantized energy levels of the classical electron motion in the vicinity of the saddle point obtained with an approximation of the potential. The results give clear evidence for signatures of the transition state in quantum spectra.