Dynamical disorder in cords: A diffusive behavior in the velocity

It is proved that the expectation value of the kinetic energy becomes unbounded in time for a finite cord with dynamical disorder (perturbation random in time). This behavior is opposed to the other without disorder (periodic perturbation), where the energy remains bounded outside the resonance regime. The growth of the energy expectation value is given explicitly, and a diffusive behavior in the velocity was found.