HYDRODYNAMIC LIMIT FOR A DISORDERED HARMONIC CHAIN

Cedric Bernardin (1) , François Huveneers (2) , Stefano Olla (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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. Furthermore it follows from our proof that the temperature profile does not evolve in any space-time scale.

Mots clés: Anderson Localization; Euler equations; Hydrodynamic limits random environment

Domaines: Mécanique statistique [cond-mat.stat-mech]; Probabilités [math.PR]; Physique mathématique [math-ph]

Cedric Bernardin, François Huveneers, Stefano Olla. HYDRODYNAMIC LIMIT FOR A DISORDERED HARMONIC CHAIN. Communications in Mathematical Physics, 2019, 365 (1), pp.215-237. ⟨10.1007/s00220-018-3251-4⟩. ⟨hal-01721245v3⟩