Abstract
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{é}vy process. For a critical value of the coupling, the energy diffusion is described by a family of L{é}vy processes which interpolates between these two processes.
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