On semiclassical dispersion relations of Harper-like operators

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dc.creatorPankrashkin, Konstantin
dc.date2004-01-28
dc.date2004-10-20
dc.date.accessioned2026-07-07T06:26:57Z
dc.date.available2026-07-07T06:26:57Z
dc.descriptionWe describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical Hamiltonian is studied for the case of integer flux. We derive asymptotic formula for the dispersion relations, the width of bands and gaps, and show how geometric characteristics and the absence of symmetries of the Hamiltonian influence the form of the energy bands.
dc.description13 pages, 8 figures; final version, to appear in J. Phys. A (2004)
dc.identifierhttps://arxiv.org/abs/math-ph/0401049
dc.identifierhttp://arxiv.org/abs/math-ph/0401049
dc.identifierwith minor changes published in J. Phys. A 37 (2004) 11681-11698
dc.identifierdoi:10.1088/0305-4470/37/48/010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97277
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject81Q20
dc.titleOn semiclassical dispersion relations of Harper-like operators
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