Molecular dynamics at an energy-level crossing

Philippe Briet (1, 2) , André Martinez (3)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E8 Dynamique quantique et analyse spectrale
3 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna

This paper is a continuation of a previous work about the study of the survival probability modelizing the molecular predissociation in the Born-Oppenheimer framework. Here we consider the critical case where the reference energy corresponds to the value of a crossing of two electronic levels, one of these two levels being confining while the second dissociates. We show that the survival probability associated to a certain initial state is a sum of the usual time-dependent exponential contribution, and a reminder term that is jointly polynomially small with respect to the time and the semiclassical parameter. We also compute explicitly the main contribution of the remainder.

Domaines: Physique mathématique [math-ph]

Philippe Briet, André Martinez. Molecular dynamics at an energy-level crossing. Journal of Differential Equations, 2019, 267 (10), pp.5662-5700. ⟨10.1016/j.jde.2019.06.004⟩. ⟨hal-01963156⟩