Quantum evolution in the regime of quantum wells in a semiclassical island with artificial interface conditions (Q2924882)

The aim of the paper is to provide a rigorous justification to the new approach to adiabatic evolution problem for the shape of resonances in models of resonant heterostructures based on the spectral analysis of a semiclassical one dimensional island Laplacian with artificial interface conditions at the boundary of the support of the potential. First of all the perturbed Laplacian is defined and Krein-like resolvent formulas are obtained. Then the shape of resonances are introduced and weighted resolvent estimates around the asymptotic resonant energy and trace estimates in the quantum wells case are proved. Finally one shows that the time propagator is stable with respect to a non-selfadjoint perturbation parametrized through infinitesimal functions of the semiclassical parameter.