Inverse transmission problems for magnetic Schr\"odinger operators

TL;DR

This paper investigates inverse transmission problems for magnetic Schr"odinger operators, demonstrating unique determination of obstacles, potentials, and transmission coefficients from boundary or scattering data in bounded and unbounded domains.

Contribution

It establishes the first uniqueness results for inverse transmission problems involving magnetic Schr"odinger operators in both bounded and unbounded settings.

Findings

Unique determination of obstacles and potentials from boundary data

Recovery of transmission coefficients from boundary measurements

Identification of magnetic and electric fields inside obstacles

Abstract

This paper is concerned with the study of inverse transmission problems for magnetic Schr\"odinger operators on bounded domains and in all of the Euclidean space, in the self-adjoint case. Assuming that the magnetic and electric potentials are known outside of a transparent obstacle, in the bounded domain case, we show that the obstacle, the transmission coefficients, as well as the magnetic field and electric potential inside the obstacle are uniquely determined from the knowledge of the set of the Cauchy data for the transmission problem, given on an open subset of the boundary of the domain. In the case of the transmission scattering problem, we obtain the same conclusion, when the scattering amplitude at a fixed frequency is known. The problems studied in this work were proposed in [15].