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Stability of energy gaps under variations of the magnetic field. (English) Zbl 0607.46049
It is proved that the location of the spectrum of the one-body Schrödinger operator is stable under small variations of the magnetic field. It is not supposed that the potential or the magnetic field vanishes at infinity. The potential is not supposed to be periodic so the results apply to crystalline and amorphous solids as well.

46N99 Miscellaneous applications of functional analysis
47F05 General theory of partial differential operators
81Q15 Perturbation theories for operators and differential equations in quantum theory
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[1] ObermairG. M. and SchellenhuberH. J., Phys. Rev. 23B, 5185 (1981).
[2] Dana, I., Avron, J., and Zak, J., ?Quantized Hall Conductance in a Perfect Crystal?. Preprint Technion-Phys. 84-27.
[3] VockE. and HunzikerW., Commun. Math. Phys. 83, 281 (1982). · Zbl 0528.35023
[4] AvronJ., HerbstI., and SimonB., Duke. Math. J. 45, 847 (1978). · Zbl 0399.35029
[5] AngelescuN., BundaruM., and NenciuG., Commun. Math. Phys. 42, 9 (1975).
[6] ReedM. and SimonB., Methods of Modern Mathematical Physics II, Academic Press, New York, 1975.
[7] Avron, J. and Simon, B., ?Stability of Gaps for Periodic Potentials under Variations of the Magnetic Field?, to appear in J. Phys. A. · Zbl 0586.35084
[8] CourantR. and HilbertD., Methods of Mathematical Physics II, Interscience, New York, 1962.
[9] SpainB., Vector Analysis, Van Nostrand, London, 1965.
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