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Properties of the DiracWeyl operator with a strongly singular gauge potential
Title:  Properties of the DiracWeyl operator with a strongly singular gauge potential 
Authors:  Arai, Asao Browse this author 
Issue Date:  Aug1992 
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 DiracWeyl 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 zeroenergy state. For each of selfadjoint realizations of the DiracWeyl operator, the number of the zeroenergy 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 zeroenergy states, does not hold. It is also proven that the spectrum of every selfadjoint extension of the minimal DiracWeyl 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
