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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.
