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Molecular dynamics at an energy-level crossing

Authors :: André Martinez
Philippe Briet
Centre de Physique Théorique - UMR 7332 (CPT)
Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
CPT - E8 Dynamique quantique et analyse spectrale
Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO)
Université de Bologne
Briet P.
Martinez A.
Source :: Journal of Differential Equations, Journal of Differential Equations, 2019, 267 (10), pp.5662-5700. ⟨10.1016/j.jde.2019.06.004⟩, Journal of Differential Equations, Elsevier, 2019, 267 (10), pp.5662-5700. ⟨10.1016/j.jde.2019.06.004⟩
Publication Year :: 2019
Publisher :: Elsevier BV, 2019.
Abstract: 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.<br />37 pages, 1 figure