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- W2078013642 abstract "We derive analytically the spectrum for the Schrodinger equation for quasiperiodic systems with two length scales: one large ``macroscopic'' scale [e.g., a cos(2ensuremath{pi}x/ensuremath{lambda})] and one small ``microscopic'' scale [e.g., v cos(2ensuremath{pi}x)]. The phase diagram includes regimes with exponentially narrow gaps due to the slowly varying potential, regimes where the rapidly varying potential amplifies these narrow gaps, and regimes with exponentially narrow ``Landau bands.'' The full ``devil's-staircase'' spectrum with gaps at wave vectors q=mensuremath{pi}+nensuremath{pi}/ensuremath{lambda} develops in a hierarchical manner as a increases. The results apply to systems with superlattices, to celestial orbits with two periodic perturbations, to systems with slowly varying lattice distortions, and, in particular, to quasi-one-dimensional magnets such as bis(tetramethyltetraselenafulvalene) perchlorate [(TMTSF${)}_{2}$${mathrm{ClO}}_{4}$] in magnetic fields, where our findings may provide insight into the experimentally observed cascade of phase transitions." @default.
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- W2078013642 date "1986-08-01" @default.
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- W2078013642 title "Spectra and gap amplification for systems with two widely different incommensurate periodicities" @default.
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- W2078013642 doi "https://doi.org/10.1103/physreva.34.1392" @default.
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