Resistance of a one-dimensional quasicrystal: Power-law growth

Abstract
Properties of the electrical resistance of a one-dimensional quasicrystal, whose structure is governed by the Fibonacci rule, are studied by means of the Landauer formula. In particular, it is shown that the growth of the resistance with sample length is bounded by a power law for certain energies. More specifically, the resistance is shown to grow with sample length not as a single power, but with a spectrum of exponents. These exact results are illustrated by examples. It is conjectured that such behavior is typical for the entire spectrum.