Ballistic dynamics of Dirac particles in electro-magnetic fields

Investigating properties of two-dimensional Dirac operators coupled to an electric and a magnetic field (perpendicular to the plane) requires in general unbounded (vector-) potentials. If the system has a certain symmetry, the fields can be described by one-dimensional potentials $V$ and $A$. Assuming that $\mathrm{\mid }A\mathrm{\mid }<\mathrm{\mid }V\mathrm{\mid }$ outside some arbitrary large ball, we show that absolutely continuous states of the effective Dirac operators spread ballistically. These results are based on well-known methods in spectral dynamics together with certain new Hilbert-Schmidt bounds. We use Lorentz boosts to derive these new estimates.