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arXiv · 0802.1414

Semiclassical reduction for magnetic Schroedinger operator with periodic zero-range potentials and applications

Bernard Helffer·Konstantin Pankrashkin
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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.

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Bernard Helffer, Konstantin Pankrashkin. 2008-09-12. Semiclassical reduction for magnetic Schroedinger operator with periodic zero-range potentials and applications. https://doi.org/10.3233/asy-2008-0923

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