Ihsan Topaloğlu · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27218 · cited by 0 works (OpenAlex) · open-access PDF
Kami mempelajari masalah optimasi bentuk yang diperkenalkan oleh Mazzoleni, Muratov, dan Ruffini sebagai model untuk kubit muatan superkonduktif, di mana nilai diri Dirichlet pertama dari seperangkat volume yang ditentukan bersaing dengan energi diri Coulomb dari keadaan tanah. Kami membuktikan bahwa, untuk muatan yang cukup kecil, bola adalah minimalis yang unik, dan bahwa defisit energi dari gangguan yang mempertahankan volume dan berpusat bola sebanding dengan norma persegi $H^{1/2}$ dari grafik batas, dengan konstan independen dari muatan.
Machine translation (Meta M2M100); the English original follows.
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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