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Hydrodynamic Limit for a Disordered Harmonic Chain

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Abstract

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.

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Correspondence to Stefano Olla.

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Communicated by H. Spohn

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Bernardin, C., Huveneers, F. & Olla, S. Hydrodynamic Limit for a Disordered Harmonic Chain. Commun. Math. Phys. 365, 215–237 (2019). https://doi.org/10.1007/s00220-018-3251-4

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  • DOI: https://doi.org/10.1007/s00220-018-3251-4

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