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It is well known that the contribution of harmonic phonons to the thermalconductivity of 1D systems diverges with the harmonic chain length $L$(explicitly, increases with $L$ as a power-law with a positive power).Furthermore, within various one-dimensional models containing disorder it wasshown that this divergence persists, with the thermal conductivity scaling as$\sqrt{L}$ under certain boundary conditions, where $L$ is the length of theharmonic chain. Here we show that when the chain is weakly coupled to the heatreservoirs and there is strong disorder this scaling can be violated. We find aweaker power-law dependence on $L$, and show that for sufficiently strongdisorder the thermal conductivity stops being anomalous -- despite bothdensity-of-states and the diverging localization length scaling anomalously.Surprisingly, in this strong disorder regime two anomalously scaling quantitiescancel each other to recover Fourier's law of heat transport.

Thermal conductivity in 1d: disorder-induced transition from anomalous to normal scaling