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Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise

Jara, Milton; Komorowski, Tomasz; Olla, Stefano (2015), Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise, Communications in Mathematical Physics, 339, 2, p. 407-453. 10.1007/s00220-015-2417-6

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1402.2988v3
Date
2015
Journal name
Communications in Mathematical Physics
Volume
339
Number
2
Publisher
Springer
Published in
Paris
Pages
407-453
Publication identifier
Metadata
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Author(s)
Jara, Milton
Komorowski, Tomasz
Olla, Stefano cc
Abstract (EN)
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 ∂tu=−|Δ|3/4u. 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).
Subjects / Keywords
Thermal conductivity; fractionnal diffusion; harmonic oscillators