Spectral stability under tunneling

We study the spectral properties of multiple well Schrodinger operators on ℝn. We give in particular upper bounds on energy shifts due to tunnel effect and localization properties of wave packets. Our methods are based on Agmon type estimates for resolvents in classically forbidden regions and geometric perturbation theory. Our results are valid also for an infinite number of wells, arbitrary spectral type and in non-semi-classical regimes.