An optimization problem for $\delta'$ leaky stars

Abstract:We consider singular Schrödinger operators with an attractive $\delta'$ interaction of strength $\beta$ 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 $\delta$ interaction star, the other general based on Birman-Schwinger technique.

Spectral Theory (math.SP); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Quantum Physics (quant-ph)

arXiv:2610.15771 [math.SP]

(or arXiv:2610.15771v1 [math.SP] for this version)

https://doi.org/10.48550/arXiv.2610.15771 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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