On semiclassical dispersion relations of Harper-like operators

Details On semiclassical dispersion relations of Harper-like operators On semiclassical dispersion relations of Harper-like operators

2004-01-28

arxiv.org/abs/math-ph/0401049v2

with minor changes published in J. Phys. A 37 (2004) 11681-11698

Physics

Mathematical Physics

13 pages, 8 figures; final version, to appear in J. Phys. A (2004)

Scientific paper

10.1088/0305-4470/37/48/010

We 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.

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