 02379 G. D. Raikov
 Spectral Asymptotics for the Perturbed 2D Pauli
Operator with Almost Periodic Magnetic Fields.
I. NonZero Mean Value of the Magnetic Field
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Sep 13, 02

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Abstract. We consider the Pauli operator $H(b,V)$ acting in $L^2({\mathbb R}^2;
{\mathbb C}^2)$. We describe a class of admissible magnetic fields
$b$ such that the ground state of the unperturbed operator $H(b,0)$
which coincides with the origin, is an isolated eigenvalue of infinite
multiplicity. In particular, this class includes certain almost
periodic functions of nonzero mean value. Under the assumption that
the matrixvalued electric potential $V$ has a definite sign and decays
at infinity, we invastigate the asymptotic distribution of the discrete
spectrum of $H(b,V)$ accumulating to the origin. We obtain different
asymptotic formulae valid respectively in the cases of powerlike decay
of $V$, exponential decay of $V$, or compact support of $V$.
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