Determining asymptotics of magnetic fields from fixed energy scattering data

Article type: Research Article

Authors: Joshi, Mark S.^; | Sá Barreto, Antônio

Affiliations: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK E‐mail: joshi@dpmms.cam.ac.uk | Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA E‐mail: sabarre@math.purdue.edu

Note: [] Corresponding author.

Abstract: The problem of recovering the asymptotics of a short range perturbation of the Euclidean Laplacian on \mathbb{R}^n from fixed energy scattering data is studied. It is shown that for n \geq 3 the asymptotics of a magnetic potential are determined, modulo Gauge invariance, by its scattering matrix at a fixed non‐zero energy. This result also holds for a wide class of scattering manifolds.

Keywords: Scattering theory, conormal, Lagrangian

Journal: Asymptotic Analysis, vol. 21, no. 1, pp. 61-70, 1999