Ihsan Topaloğlu · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27218 · cited by 0 works (OpenAlex) · open-access PDF
We study the shape optimization problem introduced by Mazzoleni, Muratov, and Ruffini as a model for a superconducting charge qubit, in which the first Dirichlet eigenvalue of a set of prescribed volume competes with the Coulomb self-energy of the ground state. We prove that, for sufficiently small charge, the ball is the unique minimizer, and that the energy deficit of a volume-preserving and centered perturbation of the ball is comparable to the squared $H^{1/2}$ norm of the boundary graph, with constants independent of the charge. We also obtain the corresponding results for the quadratic Hartree--Ohta--Kawasaki model.
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Topics: Ball (mathematics), Mathematics, Quadratic equation, Mathematical analysis, Eigenvalues and eigenvectors, Boundary value problem
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