G. D. Raikov
Spectral Asymptotics for the Perturbed 2D Pauli
Operator with Almost Periodic Magnetic Fields.
I. Non-Zero Mean Value of the Magnetic Field
(235K, ps.gz)
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 non-zero mean value. Under the assumption that
the matrix-valued 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 power-like decay
of $V$, exponential decay of $V$, or compact support of $V$.