Inverse scattering for the magnetic Schr\"odinger operator on surfaces   with Euclidean ends
  We prove a fixed frequency inverse scattering result for the magnetic Schr\"odinger operator (or connection Laplacian) on surfaces with Euclidean ends. We show that, under suitable decaying conditions, the scattering matrix for the operator determines both the gauge class of the connection and the zeroth order potential. 
Valter Pohjola and Leo Tzou
math.AP math-ph math.MP