  We investigate the macroscopic behavior of the disordered harmonic chain of
oscillators, through energy diffusion. The Hamiltonian dynamics of the system
is perturbed by a degenerate conservative noise. After rescaling space and time
diffusively, we prove that energy fluctuations in equilibrium evolve according
to a linear heat equation. The diffusion coefficient is obtained from the
non-gradient Varadhan's approach, and is equivalently defined through the
Green-Kubo formula. Since the perturbation is very degenerate and the symmetric
part of the generator does not have a spectral gap, the standard non-gradient
method is reviewed under new perspectives.
