Self-Similarity and Localization

Details Self-Similarity and Localization Self-Similarity and Localization

1995-05-17

arxiv.org/abs/cond-mat/9505072v1

Physics

Condensed Matter

4 pages, RevTeX, 2 figures included

Scientific paper

10.1103/PhysRevLett.75.2762

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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