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

在网络上支撑的具有δ相互作用的磁性薛定谔算子的近似

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Abstract

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

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