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An optimization problem for $δ'$ leaky stars

Year: 2026

Type: preprint

Abstract: We consider singular Schrödinger operators with an attractive $δ'$ interaction of strength $β$ supported by a star graph and prove that the ground-state eigenvalue is uniquely maximized by stars of the maximum symmetry. Two different proofs are presented, one for an even number of edges using a comparison to the $δ$ interaction star, the other general based on Birman-Schwinger technique.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.15771

Author: Exner, Pavel

Institutions: Czech Academy of Sciences, Nuclear Physics Institute, Czech Technical University in Prague

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221829628

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