On semiclassical dispersion relations of Harper-like operators
Mathematical Physics
2007-05-23 v2 math.MP
Spectral Theory
Abstract
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.
Cite
@article{arxiv.math-ph/0401049,
title = {On semiclassical dispersion relations of Harper-like operators},
author = {Konstantin Pankrashkin},
journal= {arXiv preprint arXiv:math-ph/0401049},
year = {2007}
}
Comments
13 pages, 8 figures; final version, to appear in J. Phys. A (2004)