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Semiclassical reduction for magnetic Schrödinger operator with periodic zero-range potentials and applications. (English) Zbl 1185.35043
Authors’ abstract: The two-dimensional Schrödinger operator with a uniform magnetic field and a periodic zero-range potential is considered. For weak magnetic fields and a weak coupling 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.
MSC:
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
47G30 Pseudodifferential operators
47N50 Applications of operator theory in the physical sciences
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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