Widths of highly excited resonances in multidimensional molecular predissociation

TL;DR

This paper analyzes the widths of highly excited resonances in multidimensional molecular predissociation using semiclassical analysis, providing bounds on resonance widths through advanced microlocal techniques.

Contribution

It introduces a novel approach to estimate resonance widths in multidimensional systems with complex potentials using Carleman estimates and microlocal analysis.

Findings

Established an optimal lower bound on resonance widths.

Applied advanced microlocal techniques to molecular predissociation.

Extended semiclassical resonance analysis to multidimensional systems.

Abstract

We investigate the simple resonances of a 2 by 2 matrix of n-dimensional semiclassical Shr\"odinger operators that interact through a first order differential operator. We assume that one of the two (analytic) potentials admits a well with non empty interior, while the other one is non trapping and creates a barrier between the well and infinity. Under a condition on the resonant state inside the well, we find an optimal lower bound on the width of the resonance. The method of proof relies on Carleman estimates, microlocal propagation of the microsupport, and a refined study of a non involutive double characteristic problem in the framework of Sj\"ostrand's analytic microlocal theory.