Resistance of one-dimensional quasicrystals

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Abstract

One-dimensional quasiperiodic systems are often based on an inflation rule giving rise to a recursion formula on the transfer matrices. It is shown in a general setting, that the norm growth of these matrices can be evaluated. A consequence is, for instance, a purely critical regime (namely polynomial bounds in function of the sample size) for the electrical resistance, when the energy is in the spectrum. This solves a conjecture by Sutherland and Kohmoto.

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    1

    Also at: Université de Provence, Marseille, France.

    2

    Also at: Maîtrise de Physique, Université de Provence, Marseille, France.

    3

    Also at: Université d'Aix-Marseille II, Marseille, France.

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