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Optimal Potentials for Quantum Graphs
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22019 (English)In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 20, no 5, p. 1517-1542Article in journal (Refereed) Published
Abstract [en]

Schrödinger operators on metric graphs with delta couplings at the vertices are studied. We discuss which potential and which distribution of delta couplings on a given graph maximise the ground state energy, provided the integral of the potential and the sum of strengths of the delta couplings are fixed. It appears that the optimal potential if it exists is a constant function on its support formed by a set of intervals separated from the vertices. In the case where the optimal configuration does not exist explicit optimising sequences are presented.

Place, publisher, year, edition, pages
2019. Vol. 20, no 5, p. 1517-1542
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Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:su:diva-169281DOI: 10.1007/s00023-019-00783-6ISI: 000465376800005OAI: oai:DiVA.org:su-169281DiVA, id: diva2:1321205
Available from: 2019-06-07 Created: 2019-06-07 Last updated: 2019-06-07Bibliographically approved

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Kurasov, PavelSerio, Andrea
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