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


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.


Lyapunov Exponent Random Matrix Heat Bath Heat Current Joint Behavior 
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Authors and Affiliations

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

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