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Hydrodynamic Limit for a Disordered Harmonic Chain

Bernardin, Cédric; Huveneers, François; Olla, Stefano (2018), Hydrodynamic Limit for a Disordered Harmonic Chain, Communications in Mathematical Physics, 365, 1, p. 215-237. 10.1007/s00220-018-3251-4

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Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01721245
Date
2018
Journal name
Communications in Mathematical Physics
Volume
365
Number
1
Publisher
Springer
Pages
215-237
Publication identifier
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Author(s)
Bernardin, Cédric
Laboratoire Jean Alexandre Dieudonné [LJAD]
Huveneers, François
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / Keywords
Euler equations, Anderson localization; Hydrodynamic limits radom environment