ON QUANTUM STABILITY FOR SYSTEMS UNDER QUASI-PERIODIC PERTURBATIONS

We prove that the spectrum defined in terms of the autocorrelation fun ction of a harmonic subject to a quasiperiodic perturbation, is, at re sonance, transient absolutely continuous, covering the whole line. In the nonresonant case, and under some supplementary Diophantine conditi on, it is pure point, coinciding with the spectrum of a special almost -periodic function.