Semiclassical reduction for magnetic Schroedinger operator with periodic zero-range potentials and applications
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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.
31 pages, minor revision (typos corrected, references updated), accepted in Asymptotic Analysis
31 pages, minor revision (typos corrected, references updated), accepted in Asymptotic Analysis