Abstract
We find upper and lower bounds for the transmission coefficient of a chain of random masses. Using these bounds we show that the heat conduction in such a chain does not obey Fourier's law: For different temperatures at the ends of a chain containingN particles the energy flux falls off likeN −1/2 rather thanN −1.
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Communicated by J. L. Lebowitz
Research supported by a ZWO fellowship and in part by U.S.A.F.O.S.R. grant no. 78-3522
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Verheggen, T. Transmission coefficient and heat conduction of a harmonic chain with random masses: Asymptotic estimates on products of random matrices. Commun.Math. Phys. 68, 69–82 (1979). https://doi.org/10.1007/BF01562542
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DOI: https://doi.org/10.1007/BF01562542