Propagation of Coherent States through Conical Intersections

TL;DR

This paper studies how wave packets propagate through conical intersections in quantum systems, providing explicit transition formulas and phase transformations, extending previous Gaussian-focused results to more general settings.

Contribution

It introduces a general framework for analyzing wave packet propagation through conical intersections, with explicit transition formulas and phase computations, applicable beyond Gaussian wave packets.

Findings

Derived explicit transition formulas for wave packets crossing conical intersections.

Provided precise phase transformation calculations during the crossing.

Extended analysis to more general wave packets beyond Gaussian cases.

Abstract

In this paper, we analyze the propagation of a wave packet through a conical intersection. This question has been addressed for Gaussian wave packets in the 90s by George Hagedorn and we consider here a more general setting. We focus on the case of Schr{\"o}dinger equation but our methods are general enough to be adapted to systems presenting codimension 2 crossings and to codimension 3 ones with specific geometric conditions. Our main Theorem gives explicit transition formulas for the profiles when passing through a conical crossing point, including precise computation of the transformation of the phase. Its proof is based on a normal form approach combined with the use of superadiabatic projectors and the analysis of their degeneracy close to the crossing.