We consider a chain of weakly harmonic coupled oscillators perturbed by a conservative noise. We show that by tuning accordingly the coupling constant energy can diffuse like a Brownian motion or superdiffuse like a maximally 3/2-stable asymmetric L{ \'e}vy process. For a critical value of the coupling, the energy diffusion is described by a family of L{ \'e}vy processes which interpolates between these two processes.
Categories: math.PR cond-mat.stat-mech math-ph math.MP