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Title: Heat conduction and phonon localization in disordered harmonic crystals
Authors: Kundu, Anupam
Chaudhuri, A.
Roy, Dibyendu
Dhar, Abhishek
Lebowitz, J.L.
Spohn, Herbert
Keywords: Anderson localization
lattices glasses
Issue Date: May-2010
Publisher: EDP Sciences / IOP / Società Italiana di Fisica
Citation: Europhysics Letters, 2010, Vol. 90, p40001
Abstract: We investigate the steady state heat current in two and three dimensional isotopically disordered harmonic lattices. Using localization theory as well as kinetic theory we estimate the system size dependence of the current. These estimates are compared with numerical results obtained using an exact formula for the current given in terms of a phonon transmission function, as well as by direct nonequilibrium simulations. We find that heat conduction by high-frequency modes is suppressed by localization while low-frequency modes are strongly affected by boundary conditions. Our {\color{black}heuristic} arguments show that Fourier's law is valid in a three dimensional disordered solid except for special boundary conditions. We also study the pinned case relevant to localization in quantum systems and often used as a model system to study the validity of Fourier's law. Here we provide the first numerical verification of Fourier's law in three dimensions. In the two dimensional pinned case we find that localization of phonon modes leads to a heat insulator.
Description: Restricted Access. An open-access version is available at (one of the alternative locations)
ISSN: 1286-4854-(Online)
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Copyright: 2010 EPLA
Appears in Collections:Research Papers (TP)

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