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Journal Article

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

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Fleischmann,  Ragnar       
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Kottos,  Tsampikos
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Bodyfelt, J. D., Zheng, M. C., Fleischmann, R., & Kottos, T. (2013). Scaling theory of heat transport in quasi-one-dimensional disordered harmonic chains. Physical Review E, 87(2): 020101(R). doi:10.1103/PhysRevE.87.020101.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-1029-2
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.