Long time growth of Sobolev norms in time dependent semiclassical anharmonic oscillators

Emanuele Haus, Alberto Maspero

We consider the semiclassical Schrödinger equation on ${\mathbb{R}}^d$ given by $$\mathrm{i}\hslash {\partial }_t\psi =\left(-\frac{{\hslash }^2}{2}\Delta +W_l(x)\right)\psi +V(t,x)\psi ,$$ where $W_l$ is…