Advanced Search

This article studies the asymptotic behavior of the number $N\left(\lambda \right)$ of the negative eigenvalues $\<-\lambda$ as $\lambda \to +0$ of the two dimensional Pauli operators with electric potential $V\left(x\right)$ decaying at $\infty$ and with nonconstant magnetic field $b\left(x\right)$, which is assumed to be bounded or to decay at $\infty$. In particular, it is shown that $N\left(\lambda \right)=(1/2\pi ){\int }_{V\left(x\right)\>\lambda }b\left(x\right)dx(1+o\left(1\right))$, when $V\left(x\right)$ decays faster than $b\left(x\right)$ under some additional conditions.