Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise
Milton Jara, Tomasz Komorowski, Stefano Olla · Communications in Mathematical Physics · 2015
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 $${\partial_t u = -|\Delta|^{3/4}u}$$ . For a pinned system we prove that its energy evolves diffusively, generalizing some results of Basile and Olla (J. Stat. Phys. 155(6):1126–1142, 2014).