  In this work we consider the KAM renormalizability problem for small
pseudodifferential perturbations of the semiclassical isochronous transport
operator with Diophantine frequencies on the torus. Assuming that the symbol of
the perturbation is real analytic and globally bounded, we prove convergence of
the quantum Lindstedt series and describe completely the set of semiclassical
measures and quantum limits of the renormalized system. Each of these measures
is given by symplectic deformation of the Haar measure on an invariant torus
for the unperturbed classical system.
