ESTIMATES ON THE MOLECULAR DYNAMICS FOR THE PREDISSOCIATION PROCESS

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

1 CPT - Centre de Physique Théorique - UMR 7332
2 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: quantum evolution; Born-Oppenheimer approximation; Resonances; eigenvalue cross-ing; survival probability

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

Philippe Briet, André Georges Martinez. ESTIMATES ON THE MOLECULAR DYNAMICS FOR THE PREDISSOCIATION PROCESS. 2015. ⟨hal-01132939v2⟩