Estimates on the molecular dynamics for the predissociation process

TL;DR

This paper analyzes the molecular predissociation process using semi-classical matrix Schrödinger operators, demonstrating that survival probabilities are primarily exponential with negligible correction terms, applicable in high-dimensional and resonance-rich scenarios.

Contribution

It provides a rigorous estimate of survival probabilities in molecular predissociation, accounting for complex resonances and high-dimensional cases within the semiclassical framework.

Findings

Survival probability follows an exponential decay with exponentially small correction.

Results hold in any spatial dimension and with infinitely many resonances.

Applicable to general molecules under the Born-Oppenheimer approximation.

Abstract

We study the survival probability associated with a semi-classical matrix Shr\"odinger 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.