Semiclassical reduction for magnetic Schroedinger operator with periodic zero-range potentials and applications
Mathematical Physics
2009-05-24 v2 math.MP
Abstract
The two-dimensional Schroedinger operator with a uniform magnetic field and a periodic zero-range potential is considered. For weak magnetic fields we reduce the spectral problem to the semiclassical analysis of one-dimensional Harper-like operators. This shows the existence of parts of Cantor structure in the spectrum for special values of the magnetic flux.
Cite
@article{arxiv.0802.1414,
title = {Semiclassical reduction for magnetic Schroedinger operator with periodic zero-range potentials and applications},
author = {Bernard Helffer and Konstantin Pankrashkin},
journal= {arXiv preprint arXiv:0802.1414},
year = {2009}
}
Comments
31 pages, minor revision (typos corrected, references updated), accepted in Asymptotic Analysis