Time delay in scattering by potentials and by magnetic fields with two supports at large separation

We study the asymptotic behavior of the time delay (defined as the trace of the Eisenbud-Wigner time delay operator) for scattering by potential and by magnetic field with two compact supports as the separation of supports goes to infinity. The emphasis is placed on analyzing how different the asymptotic formulae are in potential and magnetic scattering. The difference is proper to scattering in two dimensions.