Reducibility of Schrodinger equation on a Zoll manifold with unbounded potential

In this article we prove a reducibility result for the linear Schrodinger equation on a Zoll manifold with quasi-periodic in time pseudo-differential perturbation of order less or equal than $1/2$. As far as we know, this is the first reducibility results for an unbounded perturbation of a linear system which is not integrable.