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Updated: May 13, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Scaling theory of heat transport in quasi-one-dimensional disordered harmonic chains
Joshua D Bodyfelt1, Mei C Zheng, Ragnar Fleischmann
1Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA.
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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