Growth of Sobolev norms for completely resonant quantum harmonic oscillators on ${\mathbb{R}}^2$

Beatrice Langella, Alberto Maspero, Maria Teresa Rotolo

We consider time dependently perturbed quantum harmonic oscillators in ${\mathbb{R}}^2$: $$ {\rm i} \partial_t u=\frac12(-\partial_{x_1}^2-\partial_{x_2}^2 + x_1^2+x_2^2)u +V(t, x, D…