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Session 34. SPDE: stochastic analysis and dynamics
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Energy transport in an infinite chain of harmonic oscillators with a degenerate noise |
Tomasz Komorowski, IMPAN, Warsaw, Poland
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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 a fractional
diffusion governed by \(-|\Delta|^{3/4}\). For a pinned system we prove
that energy evolves diffusively, generalizing some of the earlier results contained in [1]. This is a joint work with S. Olla (CEREMADE, Univ. Paris-Dauphine) and M. Jara (IMPA, Rio de Janeiro).
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References- G. Basile, S. Olla, Energy Diffusion in Harmonic System with Conservative Noise, J. Stat. Phys., 155, no. 6, 1126-1142, 2014,
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