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Self-Similarity and Localization

Jukka A. Ketoja·Indubala I. Satija
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Abstract

The localized eigenstates of the Harper equation exhibit universal self-similar fluctuations once the exponentially decaying part of a wave function is factorized out. For a fixed quantum state, we show that the whole localized phase is characterized by a single strong coupling fixed point of the renormalization equations. This fixed point also describes the generalized Harper model with next nearest neighbor interaction below a certain threshold. Above the threshold, the fluctuations in the generalized Harper model are described by a strange invariant set of the renormalization equations.

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Jukka A. Ketoja, Indubala I. Satija. 1995-05-17. Self-Similarity and Localization. https://doi.org/10.1103/physrevlett.75.2762

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