Masao Hirokawa, Osamu Ogurisu
Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field
(33K, REVTeX v3.1)
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.
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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 \(B\) (\(=\int_{\R^2}b\,dx\,dy+\sum_j\gamma_j\)).
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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.