SUPERDIFFUSION OF ENERGY IN A CHAIN OF HARMONIC OSCILLATORS WITH NOISE
Résumé
We consider a one dimensional infinite chain of harmonic 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 the solution of the fractional diffusion equation ∂ t u = −|∆| 3/4 u. For a pinned system we prove that its energy evolves diffusively, generalizing some results of [4].
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