Approximation of magnetic Schrödinger operators with $$\delta $$-interactions supported on networks
Abstract
Abstract This paper deals with the approximation of a magnetic Schrödinger operator with a singular $$\delta $$ δ -potential that is formally given by $$(i \nabla + A)^2 + Q + \alpha \delta _\Sigma $$ ( i ∇ + A ) 2 + Q + α δ Σ by Schrödinger operators with regular potentials in the norm resolvent sense. This is done for $$\Sigma $$ Σ being the finite union of $$C^2$$ C 2 -hypersurfaces, for coefficients A , Q , and $$\alpha $$ α under almost minimal assumptions such that the associated quadratic forms are closed and sectorial, and Q and $$\alpha $$ α are allowed to be complex-valued functions. In particular, $$\Sigma $$ Σ can be a graph in $$\mathbb {R}^2$$ R 2 or the boundary of a piecewise $$C^2$$ C 2 -domain. Moreover, spectral implications of the mentioned convergence result are discussed.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Approximation Theory and Sequence Spaces
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Letters in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 116
- Issue
- 2
- Pages
- 24–24
- Publication date
- 28 February 2026
- Language
- EN