Scaling analysis of quasiperiodic systems: Generalized Harper model

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Abstract
Properties of one-dimensional quasiperiodic discrete Schrödinger equations are analyzed by means of a finite-size scaling of the spectrum and the wave function. The incommensurate Harper model, which has only one Fourier component in the potential, is analyzed as an example, and some quantitative results, which are consistent with previously known qualitative features, are obtained. In addition, some universal behaviors are observed. The methods are also applied to a generalized model with the potential having two Fourier components. The existence of mobility edges is demonstrated and the phase diagram on localized and extended states is shown.