Self-Similarity and Localization

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.

4 pages, RevTeX, 2 figures included

References in corpus (3)

• Generalized Bethe Ansatz Equations for Hofstadter Problem
• Universal criterion for the breakup of invariant tori in dissipative systems
• Decimation Studies of Bloch Electrons in a Magnetic Field: Higher Order Limit Cycles Underlying the Phase Diagram

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• Fixed points of Composition Sum Operators
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