Ihsan Topaloğlu · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.27218 · cited by 0 works (OpenAlex) · open-access PDF
우리는 Mazzoleni, Muratov, and Ruffini가 초도성 충전 큐비트의 모델로 소개한 모양 최적화 문제를 연구하고, 규정된 볼륨 집합의 첫 번째 Dirichlet 자체 가치는 지상 상태의 Coulomb 자체 에너지와 경쟁한다.우리는 충분히 작은 충전을 위해 공이 독특한 최소화자이며, 볼륨 보존 및 중심 방해의 에너지 결핍은 경계 그래프의 사각형 $H^{1/2}$ 규범과 비교할 수 있다는 것을 증명합니다.
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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