Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators

Pavel Exner; Stepan Manko

doi:10.1007/s11005-014-0706-1

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arXiv · 1310.5856

Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators

Pavel Exner·Stepan Manko

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Abstract

We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex couplings, generalizing the $δ'$-interaction on the line, and show that with a suitable choice of the parameters they can be approximated in this way in the norm-resolvent sense. We also analyze spectral properties of the involved operators and demonstrate convergence of the corresponding on-shell scattering matrices.

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BibTeX RIS

Pavel Exner, Stepan Manko. 2013-10-22. Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators. https://doi.org/10.1007/s11005-014-0706-1

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