Approximation of magnetic Schrödinger operators with δ-interactions supported on networks

This paper deals with the approximation of a magnetic Schrödinger operator with a singular δ δ -potential that is formally given by (i ∇ + A)² + Q + α δ _Σ ( i ∇ + A ) 2 + Q + α δ Σ by Schrödinger operators with regular potentials in the norm resolvent sense. This is done for Σ Σ being the finite union of C² C 2 -hypersurfaces, for coefficients A , Q , and α α under almost minimal assumptions such that the associated quadratic forms are closed and sectorial, and Q and α α are allowed to be complex-valued functions. In particular, Σ Σ can be a graph in R² R 2 or the boundary of a piecewise C² C 2 -domain. Moreover, spectral implications of the mentioned convergence result are discussed.