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Hydrodynamic Limit for a Disordered Harmonic Chain

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DHC_27_07_2018s.pdf (205.4Kb)
Date
2018
Link to item file
https://hal.archives-ouvertes.fr/hal-01721245
Dewey
Sciences connexes (physique, astrophysique)
Sujet
Euler equations, Anderson localization; Hydrodynamic limits radom environment
Journal issue
Communications in Mathematical Physics
Volume
365
Number
1
Publication date
2018
Article pages
215-237
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00220-018-3251-4
URI
https://basepub.dauphine.fr/handle/123456789/17984
Collections
  • CEREMADE : Publications
Metadata
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Author
Bernardin, Cédric
199970 Laboratoire Jean Alexandre Dieudonné [JAD]
Huveneers, François
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Olla, Stefano
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum and energy converge to the solution of the Euler equations. Anderson localization decouples the mechanical modes from the thermal modes, allowing the closure of the energy conservation equation even out of thermal equilibrium. This example shows that the derivation of Euler equations rests primarily on scales separation and not on ergodicity.

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