Newest papers

Minimality and stability of the ball for the charge-qubit energy

Ihsan Topaloğlu · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27218 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

Estudiamos el problema de optimización de forma introducido por Mazzoleni, Muratov y Ruffini como un modelo para un qubit de carga superconductora, en el que el primer valor propio de Dirichlet de un conjunto de volúmenes prescritos compite con la autoenergía de Coulomb del estado del suelo. Demostramos que, para una carga suficientemente pequeña, la bola es el minimizador único, y que el déficit de energía de una perturbación centralizada y conservadora del volumen de la bola es comparable a la norma cuadrada de $H^{1/2}$ del gráfico límite, con constantes independientes de la carga.

Machine translation (Meta M2M100); the English original follows.

Abstract

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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