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Scaling theory of heat transport in quasi-one-dimensional disordered harmonic chains

Joshua D. Bodyfelt1, Mei C. Zheng1,2, Ragnar Fleischmann3, and Tsampikos Kottos1,3

  • 1Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
  • 2Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
  • 3Max Planck Institute for Dynamics and Self-organization (MPIDS), 37077 Göttingen, Germany

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Phys. Rev. E 87, 020101(R) – Published 4 February, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.020101

Abstract

We introduce a variant of the banded random matrix ensemble and show, using detailed numerical analysis and theoretical arguments, that the phonon heat current in disordered quasi-one-dimensional lattices obeys a one-parameter scaling law. The resulting β function indicates that an anomalous Fourier law is applicable in the diffusive regime, while in the localization regime the heat current decays exponentially with the sample size. Our approach opens a new way to investigate the effects of Anderson localization in heat conduction based on the powerful ideas of scaling theory.

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Outline

Information

Phys. Rev. E 87, 020101(R)– Published 4 February, 2013
  • Received 17 August 2012
Article part of CHORUS

©2013 American Physical Society

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