Metal-Insulator Transition and Scaling for Incommensurate Systems

Tight-binding models in one dimension with incommensurate potentials are studied. For the sinusoidal-potential model scaling of the spectrum is found numerically at the critical point, which separates the region where all the states are extended and the region where all the states are localized. Absence of scaling for generic potentials indicates the existence of mobility edges. An index $\delta$, which characterizes the behavior of the total width of allowed energies, is defined at the critical point. For a class of discontinuous potentials, the systems are found to be always critical.