Energy spectrum and conductance of a two-dimensional quasicrystal

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 ${\mathrm{e}}^2$/h, just like the universal conductance fluctuation in a mesoscopic random system.