A model of a two-dimensional Fibonacci lattice is presented. Numerical calculations show that there is a transition as a function of strength of potential from the regime of zero spectral measure for a strong potential to the regime of finite measure for a weak potential. The conductance fluctuates with the system size and in the strong-potential regime the fluctuation is of the order of e²/h, just like the universal conductance fluctuation in a mesoscopic random system.
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Ueda et al. (1987) studied this question.
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