Helffer, Bernard; Pankrashkin, Konstantin Semiclassical reduction for magnetic Schrödinger operator with periodic zero-range potentials and applications. (English) Zbl 1185.35043 Asymptotic Anal. 63, No. 1-2, 1-27 (2009). 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. Reviewer: Nils Ackermann (México) 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 Keywords:Schrödinger operator; periodic potential; magnetic flux; semiclassical analysis; Cantor set; Harper-like operators × Cite Format Result Cite Review PDF Full Text: DOI arXiv