English

Propagation of Coherent States through Conical Intersections

Analysis of PDEs 2023-06-28 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2112.11784,
  title  = {Propagation of Coherent States through Conical Intersections},
  author = {Clotilde Fermanian Kammerer and Stephanie Gamble and Lysianne Hari},
  journal= {arXiv preprint arXiv:2112.11784},
  year   = {2023}
}