2015/06/30 by Miguel Ballesteros, Ricardo Weder · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Cold Atom Physics and Bose-Einstein Condensates #Geometry #Inverse #Inverse problem #Inverse scattering problem #Inverse scattering transform #Klein–Gordon equation #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum electrodynamics #Quantum inverse scattering method #Quantum mechanics #Range (aeronautics) #Scattering #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:35P25 #msc:35Q40 #msc:35R30 #msc:81U40
paper · pdf · doi:10.1088/1751-8113/49/15/155302
published in Journal of Physics A Mathematical and Theoretical 49(15), 155302 (Institute of Physics) · Published version, it has been edited to improve the presentation
openalex publication_date 2016/03/02 · arxiv created 2016/03/30 · arxiv updated 2016/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The study of obstacle scattering for the Klein−Gordon equation in the presence of long-range magnetic potentials is addressed. Previous results of the authors are extended to the long-range case and the results the authors previously proved for high-momenta long-range scattering for the Schrödinger equation are brought to the relativistic scenario. It is shown that there are important differences between relativistic and non-relativistic scattering concerning the long range. In particular, it is proven that the electric potential can be recovered without assuming the knowledge of the long-range part of the magnetic potential, which has to be supposed in the non-relativistic case. The electric potential and the magnetic field are recovered from the high-momenta limit of the scattering operator, as well as fluxes modulo around the handles of the obstacle. Moreover, it is proven that for every , can be reconstructed, where is the long-range part of the magnetic potential. A simple formula for the high-momenta limit of the scattering operator is given in terms of magnetic fluxes over handles of the obstacle and long-range magnetic fluxes at infinity, that are introduced in this paper. The appearance of these long-range magnetic fluxes is a new effect in scattering theory.