On the spectrum of two-dimensional Schrödinger operators with spherically symmetric, radially periodic magnetic fields (Q1379680)

The authors investigate the spectrum of the two-dimensional Schrödinger operator \[ H=-(\partial_x - ia_1(x,y))^2- (\partial_y- ia_2(x,y))^2 + V(x,y), \] that describes the motion of charged particles in the presence of an electric field with the potential \(V(x,y)\) and a magnetic field \(B = (\partial_x a_1 - \partial_y a_2)\). Assuming that the potential \(V\) and the magnetic field \(B = b(r)\) are spherically symmetric, and \(b\) is \(p\)-periodic, the authors find that in the case \(\int_0^{\infty} b(s) ds =0\) the spectrum contains a semi-axis that consists alternately of intervals of an absolutely continuous and a dense point spectrum. Otherwise, the essential spectrum is a purely dense point spectrum. Examples include the case of a homogeneous magnetic field, \(b(r) \equiv b\).