  We consider two-dimensional Schr\"odinger operators $H$ with Aharonov-Bohm
magnetic field and an additional electric potential. We obtain an explicit
leading term of the asymptotic expansion of the unitary group $e^{-i t H}$ for
$t\to\infty$ in weighted $L^2$ spaces. In particular, we show that the magnetic
field improves the decay of $e^{-i t H}$ with respect to the unitary group
generated by non-magnetic Schr\"odinger operators, and that the decay rate in
time is determined by the magnetic flux.
