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Properties of the Dirac-Weyl operator with a strongly singular gauge potential

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83304

Title: Properties of the Dirac-Weyl operator with a strongly singular gauge potential
Authors: Arai, Asao Browse this author
Issue Date: Aug-1992
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 160
Start Page: 2
End Page: 26
Abstract: Considered is a quantum system of a charged particle moving in the plane R 2 under the influence of a perpendicular magnetic field concentrated on some fixed isolated points in R 2• Such a magnetic field is represented as a finite linear combination of the two­dimensional Dirac delta distributions and their derivatives, so that the gauge potential of the magnetic field also may be strongly singular at those isolated points. Properties of the Dirac-Weyl operator with such a singular gauge potential are investigated. It is seen that some of them depend on whether the magnetic flux is locally quantized or not. Particular attention is paid to the zero-energy state. For each of self-adjoint realizations of the Dirac­Weyl operator, the number of the zero-energy states is computed. It is shown that, in the present case, a theorem of Aharonov and Casher [Phys.Rev. A 19, 2461(1979)], which relates the total magnetic flux to the number of zero-energy states, does not hold. It is also proven that the spectrum of every self-adjoint extension of the minimal Dirac-Weyl operator is equal to R.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/68906
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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