Time dependent Quantum Perturbations uniform in the semiclassical regime

International audienceWe present a time dependent quantum perturbation result, uniformin the Planck constant, for perturbations of potentials whose gradientsare Lipschitz continuous by potentials whose gradients are only bounded a.e..Though this low regularity of the full potential is not enough to provide theexistence of the classical underlying dynamics, at variance with the quantumone, our result shows that the classical limit of the perturbed quantum dynamicsremains in a tubular neighbourhood of the classical unperturbed oneof size of order of the square root of the size of the perturbation. We treatboth Schrödinger and von Neumann-Heisenberg equations