Spectra and gap amplification for systems with two widely different incommensurate periodicities

Details Spectra and gap amplification for systems with two widely different incommensurate periodicities Spectra and gap amplification for systems with two widely different incommensurate periodicities

Aug 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrva..34.1392a&link_type=abstract

Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 34, Aug. 1986, p. 1392-1402. Research supported by the Un

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Magnets, Schroedinger Equation, Spectrum Analysis, Superlattices, Magnetic Fields, Orbits, Oscillations, Perchlorates, Phase Diagrams, Quantum Mechanics, Other Topics In Electronic Structure, Celestial Mechanics

Scientific paper

The spectrum for the Schroedinger equation is derived analytically for quasiperiodic systems with two length scales: one large 'macroscopic' scale and one small 'microscopic' scale. The phase diagram inicludes 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 certain wave vectors develops in a hierarchical manner. The results apply to systems with superlattices, to celestial orbits with two periodic pperturbations, to systems with slowly varying lattice distortions, and, in particular, to quasi-one-dimensional magnets such as bis(tetramethyltetraselenafulvalene) perchlorate in magnetic fields, where the findings may provide insight into the experimentally observed cascade of phase transitions.

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