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On the tunneling effect for magnetic Schrödinger operators in antidot lattices
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2006 (English)In: Asymptotic Analysis, ISSN 0921-7134, Vol. 48, no 1-2, 91-120 p.Article in journal (Refereed) Published
Abstract [en]

We study the Schrodinger operator (hD-A)(2) with periodic magnetic field B=curl A in an antidot lattice Omega(infinity) = R-2\boolean OR(alpha is an element of Gamma)(U+alpha). Neumann boundary conditions lead to spectrum below hinf B. Under suitable assumptions on a "one-well problem" we prove that this spectrum is localized inside an exponentially small interval in the semi-classical limit h -> 0. For this purpose we construct a basis of the corresponding spectral subspace with natural localization and symmetry properties.

Place, publisher, year, edition, pages
2006. Vol. 48, no 1-2, 91-120 p.
Keyword [en]
semi-classical analysis, tunneling effect, magnetic Schrodinger operator, periodic operator
National Category
URN: urn:nbn:se:kth:diva-37491ISI: 000237742100006ScopusID: 2-s2.0-33646722843OAI: diva2:434075

QC 20141128

Available from: 2011-08-12 Created: 2011-08-12 Last updated: 2014-11-28Bibliographically approved

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Frank, Rupert L.
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