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

Year: 2009

Type: article

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.

Source: Asymptotic Analysis

DOI: 10.3233/asy-2008-0923

Authors: Bernard Helffer, Konstantin Pankrashkin

Institutions: Université Paris-Sud, Laboratoire de Mathématiques d'Orsay, Humboldt-Universität zu Berlin

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W1744830484

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