# Rigorous scaling law for the heat current in disordered harmonic chain

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http://hdl.handle.net/10138/25718

#### Citation

Ajanki , O & Huveneers , F 2011 , ' Rigorous scaling law for the heat current in disordered harmonic chain ' , Communications in Mathematical Physics , vol. 301 , no. 3 , pp. 841-883 . https://doi.org/10.1007/s00220-010-1161-1

 Title: Rigorous scaling law for the heat current in disordered harmonic chain Author: Ajanki, Oskari; Huveneers, Francois Contributor: University of Helsinki, Department of Mathematics and Statistics Date: 2011 Language: eng Belongs to series: Communications in Mathematical Physics ISSN: 0010-3616 URI: http://hdl.handle.net/10138/25718 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 EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, 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. Subject: math-ph math.MP 80A20 (Primary), 82C44, 60J35 (Secondary) Rights:
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