Rigorous Scaling Law for the Heat Current in Disordered Harmonic Chain |
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Authors: | Oskari Ajanki François Huveneers |
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Affiliation: | 1.Department of Mathematics and Statistics,University of Helsinki,Helsinki,Finland;2.UcL, FYMA,Louvain-la-Neuve,Belgium |
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Abstract: | We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T 1 and T n . Let E J n be the steady-state energy current across the chain, averaged over the masses. We prove that E J n ~ (T 1 − T n )n −3/2 in the limit n → ∞, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices. |
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