Abstract

We consider a 2D Pauli operator with almost-periodic field b and electric potential V. First, we study the ergodic properties of H and show, in particular, that its discrete spectrum is empty if there exists a magnetic potential which generates the magnetic field b - b(0), where b(0) is the mean value of b. Next, we assume that V = 0, and investigate the zero modes of H. As expected, if b(0 )not equal 0, then generically dim Ker H = infinity. If b(0) = 0, then for each m is an element of N boolean OR {infinity}, we construct an almost-periodic b such that dim Ker H = m. This construction depends strongly on results concerning the asymptotic behavior of Dirichlet series, also obtained in the present article.