1. Propagation of Coherent States through Conical Intersections
- Author
-
Kammerer, Clotilde Fermanian, Gamble, Stephanie, Hari, Lysianne, Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Department of Mathematics, Virginia Tech [Blacksburg], Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), CNRS 80|Prime program AlgDynQua, Projet Région Bourgogne Franche-Comté - ANER - ClePh-M., ANR-18-CE40-0028,ESSED,Etudes de solutions spéciales pour des équations dispersives(2018), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), and Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Mathematics - Analysis of PDEs ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,MSC Classification 2020 : 35Q40, 35Q41, 81Q05, 81Q20,81R30 ,FOS: Mathematics ,FOS: Physical sciences ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Mathematical Physics (math-ph) ,Mathematical Physics ,Analysis of PDEs (math.AP) - 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.
- Published
- 2021