Scattering by a toroidal coil

الأصل · EN

In this paper we consider the Schrödinger operator in R³ with a long-range magnetic potential associated to a magnetic field supported inside a torus T. Using the scheme of smooth perturbations we construct stationary modified wave operators and the corresponding scattering matrix S(λ). We prove that the essential spectrum of S(λ) is an interval of the unit circle depending only on the magnetic flux ϕ across the section of T. Additionally we show that, in contrast to the Aharonov-Bohm potential in R², the total scattering cross-section is always finite. We also conjecture that the case treated here is a typical example in dimension 3.