Multifractal analysis of electronic transitions in a family of quasiperiodic potentials

We analyze the nature of extended, localized and critical states in an extension of the Aubry model where mobility edges have been reported. We calculate the multifractal spectra of exact eigenstates of this model for varying chain lengths and confirm the existence of mobility edges. Moreover we are able to show that the localized states can exhibit a behaviour rather different from the usual exponentially decaying states in a random potential. Lyapounov exponents or participation ratios are unable to produce such information. Our results also indicate that a stable multifractal distribution is a general feature of crossovers of states of different nature. This conjecture should be confirmed in other models. (author). 17 refs, 8 figs