Superdiffusion of energy in a chain of harmonic oscillators with noise

Abstract

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].

New version with corrections. Diffusion of phonon modes remouved, it will appear in a forthcoming note

References in corpus (5)

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• 3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise
• Ballistic and superdiffusive scales in macroscopic evolution of a chain of oscillators

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