Lower bound on the resolvent for trapped situations [Minoration de la résolvante dans le cas captif]

摘要

In this note, we prove an optimal universal lower bound on the truncated resolvent for semiclassical Schr?dinger operators near a trapping energy. In particular, this shows that known upper bounds for hyperbolic trapping are optimal. The proof rely on an idea of X.P. Wang, and on propagation of coherent states for Ehrenfest times.