ANDERSON TRANSITION IN THE AUBRY MODEL OF ONE-DIMENSIONAL INCOMMENSURATE SYSTEMS

Using numerical calculation, it is found that there are extended states, intermediate states and localized states in the Aubry model of one-dimensional incommensurate systems. The transition from extended states to localized states should pass through a regime in which the intermediate states exist. The regime is situated at about the potential strength V = 2t. The new result is different from that of duality theory which predicts that all states are extended for V < 2t, while, for V > 2t all states are localized; at V = 2t there exists an Anderson transition.