Weighted dispersive estimates for two-dimensional Schrödinger operators with Aharonov-Bohm magnetic field

We consider two-dimensional Schrödinger operators H with an Aharonov-Bohm magnetic field and an additional electric potential. We obtain an explicit leading term of the asymptotic expansion of the unitary group e−itH for t→∞ in weighted L2-spaces. In particular, we show that the magnetic field improves the decay of e−itH with respect to the unitary group of non-magnetic Schrödinger operators, and that the decay rate in time is determined by the magnetic flux.