A uniform quantum version of the Cherry theorem

Carlos Villegas Blas, Sandro Graffi

Consider in $L^2({\mathbb{R}}^2)$ the operator family $H(\epsilon ):=P_0(\hslash ,\omega )+\epsilon F_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $\om$, $F_0$ a bounded pseudodiffe…