|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Properties of the Dirac-Weyl operator with a strongly singular gauge potential
| Title: | Properties of the Dirac-Weyl operator with a strongly singular gauge potential |
| Authors: | Arai, Asao Browse this author |
| Issue Date: | Aug-1992 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
|
