 0480 Takuya Mine
 The AharonovBohm solenoids in a constant magnetic field
(778K, Postscript)
Mar 12, 04

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Abstract. We study the spectral properties of twodimensional magnetic Schr\"odinger
operator $H_N= (\frac{1}{i}\nabla + \a_N)^2$.
The magnetic field is given by
$\rot \a_N = B+\sum_{j=1}^N 2\pi\alpha_j \delta(zz_j)$,
where $B>0$ is a constant, $1\leq N \leq \infty$,
$0<\alpha_j<1$ $(j=1,\ldots,N)$
and the points $\{z_j\}_{j=1}^N$ are uniformly separated.
We give an upper bound for the number of eigenvalues of $H_N$
between two Landau levels or below the lowest Landau level,
when $N$ is finite.
We prove the spectral localization of $H_N$ near the spectrum of
the single solenoid operator,
when $\{z_j\}_{j=1}^N$ are far from each other,
all the values $\{\alpha_j\}_{j=1}^N$ are the same and
the boundary conditions at all $z_j$ are the same.
We give a characterization of selfadjoint extensions of
the minimal operator.
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