Nagoya Mathematical Journal

Weak Bloch property for discrete magnetic Schrödinger operators

Yusuke Higuchi and Tomoyuki Shirai

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Abstract

For a magnetic Schrödinger operator on a graph, which is a generalization of classical Harper operator, we study some spectral properties: the Bloch property and the behaviour of the bottom of the spectrum with respect to magnetic fields. We also show some examples which have interesting properties.

Article information

Source
Nagoya Math. J. Volume 161 (2001), 127-154.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631555

Mathematical Reviews number (MathSciNet)
MR1820215

Zentralblatt MATH identifier
0985.58011

Subjects
Primary: 58J99: None of the above, but in this section
Secondary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.) 39A70: Difference operators [See also 47B39] 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

Citation

Higuchi, Yusuke; Shirai, Tomoyuki. Weak Bloch property for discrete magnetic Schrödinger operators. Nagoya Math. J. 161 (2001), 127--154. https://projecteuclid.org/euclid.nmj/1114631555.


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