  We study the energy level structure of two-dimensional charged particles in
inhomogeneous magnetic fields. In particular, for magnetic anti-dots the
magnetic field is zero inside the dot and constant outside. Such a device can
be fabricated with present-day technology. We present detailed semiclassical
studies of such magnetic anti-dot systems and provide a comparison with exact
quantum calculations. In the semiclassical approach we apply the Berry-Tabor
formula for the density of states and the Borh-Sommerfeld quantization rules.
In both cases we found good agreement with the exact spectrum in the weak
magnetic field limit. The energy spectrum for a given missing flux quantum is
classified in six possible classes of orbits and summarized in a so-called
phase diagram. We also investigate the current flow patterns of different
quantum states and show the clear correspondence with classical trajectories.
