Spectral Asymptotics for the Perturbed 2D Pauli Operator with Oscillating Magnetic Fields. I. Non-Zero Mean Value of the Magnetic Field,

#### G.D. Raikov

2003, v.9, Issue 4, 775-794

ABSTRACT

We consider the Pauli operator $H(b,V)$ acting in $L^2({\r}^2; {\C}^2)$. 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. Under 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 $V$.

Keywords: spectral asymptotics,Pauli operator,magnetic field