Semiclassical scarring on tori in KAM Hamiltonian systems

We show that for almost all perturbations in a one-parameter family of KAM Hamiltonians on a smooth compact surface, for almost all KAM Lagrangian tori ${\mathrm{\Lambda }}_{\omega }$, we can find a semiclassical measure with positive mass on ${\mathrm{\Lambda }}_{\omega }$.