02-379 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) 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 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\$.

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