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Communications in Mathematical Physics

, Volume 301, Issue 3, pp 841–883 | Cite as

Rigorous Scaling Law for the Heat Current in Disordered Harmonic Chain

  • Oskari AjankiEmail author
  • François Huveneers
Article

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 1T 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.

Keywords

Lyapunov Exponent Random Matrix Heat Bath Heat Current Joint Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.UcL, FYMALouvain-la-NeuveBelgium

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