×

zbMATH — the first resource for mathematics

Weak Bloch property for discrete magnetic Schrödinger operators. (English) Zbl 0985.58011
The authors study the spectral properties of the discrete magnetic Laplacian in terms of the growth function of a graph. They also study the behaviour of the bottom of the spectrum as a function of the magnetic flux. They exhibit various examples which have interesting properties.

MSC:
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
PDF BibTeX Cite
Full Text: DOI
References:
[1] Phys. Rev B14 pp 2239– (1976)
[2] Yokohama Math. J pp 129– (1999)
[3] DOI: 10.1006/jfan.1999.3478 · Zbl 1073.47517
[4] Proc. Phys. Soc. London A 68 pp 874– (1955)
[5] in ”From local times to global geometry, control and physics” (K. D. Elworthy, ed.), Pitman Research Notes in Mathematics Series 150 pp 68– (1986)
[6] DOI: 10.1090/conm/073/954626
[7] Forum Math 1 pp 69– (1989)
[8] in ”Geometry of the spectrum” 173 pp 283– (1994)
[9] Lecture Note in Math 1201 pp 14– (1985)
[10] Methods of Modern Mathematical Physics IV (1978)
[11] J. Differ. Geom 2 pp 1– (1968) · Zbl 0162.25401
[12] DOI: 10.1215/S0012-7094-93-07114-1 · Zbl 0787.05083
[13] DOI: 10.1007/BF01234419 · Zbl 0665.46051
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.