Estimates On The Molecular Dynamics For The Predissociation Process

Philippe Briet (1, 2) , André Georges 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

We study the survival probability associated with a semi-classical matrix Shrödinger operator that models the predissociation of a general molecule in the Born-Oppenheimer approximation. We show that it is given by its usual time-dependent exponential contribution, up to a reminder term that is exponentially small (in the semiclassical parameter) with arbitrarily large rate of decay. The result applies in any dimension, and in presence of a number of resonances that may tend to infinity as the semiclassical parameter tends to 0.

Mots clés: Resonances; survival probability; eigenvalue cross-ing; quantum evolution; Born-Oppenheimer approximation

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]

Philippe Briet, André Georges Martinez. Estimates On The Molecular Dynamics For The Predissociation Process. Journal of Spectral Theory, 2017, 7 (2), pp.487-517. ⟨10.4171/JST/170⟩. ⟨hal-01132939v3⟩