1210.7648 (Gabriele Grillo et al.)

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

Gabriele Grillo, Hynek Kovarik

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.

View original: http://arxiv.org/abs/1210.7648