Spectral asymptotics for the perturbed 2D Pauli operator with almost periodic magnetic fields. I. Nonzero mean value of the magnetic field, preprint

Abstract. We consider the Pauli operator H(b, V) acting in L2 (R2;C2). We describe a class of oscillating magnetic fields b for which the ground state of the unperturbed operator H(b, 0)which coincides with the origin, is an isolated eigenvalue of infinite multiplicity. Un-der the assumption that the matrix-valued electric potential V has a definite sign and decays at infinity, we investigate 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.