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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