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arXiv · 2507.08301

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

Markus Holzmann
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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 $(i \nabla + A)^2 + Q + αδ_Σ$ by Schrödinger operators with regular potentials in the norm resolvent sense. This is done for $Σ$ being the finite union of $C^2$-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 $\mathbb{R}^2$ or the boundary of a piecewise $C^2$-domain. Moreover, spectral implications of the mentioned convergence result are discussed.

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Markus Holzmann. 2026-02-02. Approximation of magnetic Schrödinger operators with $δ$-interactions supported on networks. https://arxiv.org/abs/2507.08301

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