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

Abstract

We consider two-dimensional Schrödinger 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 $e^{-itH}$ for $t\to \infty$ in weighted $L^2$ spaces. In particular, we show that the magnetic field improves the decay of $e^{-itH}$ with respect to the unitary group generated by non-magnetic Schrödinger operators, and that the decay rate in time is determined by the magnetic flux.

To appear in J. Differential Equations