Energy growth in quantum systems with high dynamical disorder

It is argued that the energy becomes unbounded in time for systems with high dynamical disorder. Consequently the time-evolution could not be periodic or quasiperiodic. Evolution equations are formally equivalent to others found in solid state for systems with static disorder. In this way, it is a surprising result because it is opposite to others known as localization by static disorder where the time-evolution is quasiperiodic. Estimation for the time of relaxation and the diffusion constant are given explicitly. Equivalently the author's results are also valid at the classical limit with any amount of disorder. A qualitative discussion is carried out in systems with any amount of disorder.