We consider a one dimensional infinite chain of har- monic oscillators whose
dynamics is perturbed by a stochastic term conserving energy and momentum. We
prove that in the unpinned case the macroscopic evolution of the energy
converges to a fractional diffusion. For a pinned system we prove that energy
evolves diffusively, generalizing some of the results of [4].Comment: New version with corrections. Diffusion of phonon modes remouved, it
will appear in a forthcoming not
