Thermal conductance of one dimensional disordered harmonic chains

We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find non-trivial scaling of the thermal conductance with the system size. Our findings are corr...

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Bibliographic Details
Published in:arXiv.org 2019-08
Main Authors: Ash, Biswarup, Amir, Ariel, Bar-Sinai, Yohai, Oreg, Yuval, Imry, Yoseph
Format: Article
Language:English
Subjects:
Chains
Conduction heating
Conductive heat transfer
Fourier law
Localization
Longitude
Numerical analysis
Parameter identification
Phonons
Scaling
Thermal conductivity
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Summary:We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find non-trivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that a system with strong disorder, characterized by a `heavy-tailed' probability distribution, and with large impedance mismatch between the bath and the system satisfies Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.
ISSN:2331-8422
DOI:10.48550/arxiv.1908.04314