A garden of orchids: a generalized Harper equation at quadratic irrational frequencies

B. Mestel, Andrew Osbaldestin

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Abstract

We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the orchid present in the golden mean case.
Original languageEnglish
Pages (from-to)9071-9086
Number of pages16
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number9
DOIs
Publication statusPublished - Oct 2004

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