Minimal escape velocities

Abstract

We give a new derivation of the minimal velocity estimates [27] for unitary evolutions with some optimal estimates. Let H and A be selfadjoint operators on a Hilbert space H. The starting point is Mourre's inequality which is supposed to hold in form sense on the spectral subspace of H for some interval . The second assumption is that the multiple commutators are well-behaved for Then we show that, for a dense set of in and allm is contained in the spectral subspace up to an error of order t^-m in norm. We apply this general result to the case where H is a Schrödinger operator on Rⁿ and A the dilation generator, proving that is asymptotically supported in the set up to an error of order t^-m in norm.