Theory of Quantum Resonances III: Resonance Width

Abstract

The goal of this chapter is to prove exponentially small upper bounds on the imaginary part of resonances in the semiclassical regime. In Chapters 20 and 21, we proved the stability of a low-lying eigenvalue of finite multiplicity m _i ≥ 1, with respect to the perturbation H(λ, θ), Im θ > 0, for all λ sufficiently large.