Magnetic scattering at low energy in two dimensions

We study the asymptotic behavior at low energy of scattering amplitudes in two dimensional magnetic fields with compact support. The obtained result d epends on the total flux of magnetic fields. It should be noted that magnet ic potentials do not necessarily fall off rapidly at infinity. The main bod y of argument is occupied by the resolvent analysis at low energy for magne tic Schrodinger operators with perturbations of lang-range class. We can sh ow that the dimension of resonance spaces at zero energy does not exceed tw o. As a simple application, we also discuss the scattering by magnetic fiel d with small support and the convergence to the scattering amplitude by del ta-like magnetic field.