Approximation of magnetic Schrödinger operators with $δ$-interactions supported on networks
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911415443390464 |
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| author | Holzmann, Markus |
| author_facet | Holzmann, Markus |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_08301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of magnetic Schrödinger operators with $δ$-interactions supported on networks Holzmann, Markus Spectral Theory Mathematical Physics Analysis of PDEs 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. |
| title | Approximation of magnetic Schrödinger operators with $δ$-interactions supported on networks |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2507.08301 |