00-334 Masao Hirokawa, Osamu Ogurisu
Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field (33K, REVTeX v3.1) Sep 3, 00
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Abstract. It is investigated that the structure of the kernel of the Dirac-Weyl operator $$\D$$ of a charged particle in the magnetic field $$B=B_0+b$$, given by the sum of a strongly singular magnetic field $$B_0(\cdot)=\sum_j\gamma^j\delta(\cdot-a_j)$$ and a magnetic field $$b$$ with a bounded support. Here the magnetic field $$b$$ may have some singular points with the order of the singularity less than~2. % At a glance, it seems that, following Aharonov-Casher Theorem'' [Phys.Rev.A, {\bf{19}}, 1979], the dimension of the kernel of $$\D$$, $$\dim\ker\D$$, is a function of one variable, the total magnetic flux of $$B$$ ($$=\int_{\R^2}b\,dx\,dy+\sum_j\gamma_j$$). % However, since the influence of the strongly singular points occurs, $$\dim\ker\D$$ indeed is a function of several variables, the total magnetic flux and each of $$\gamma_j$$'s.

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