PreprintarXiv licencearXiv
Minimality and stability of the ball for the charge-qubit energy
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 H1/2 norm of the boundary graph, with constants independent of the charge. We also obtain the corresponding results for the quadratic Hartree--Ohta--Kawasaki model.
Related
- Second variation of the fractional torsion energy and linear stability of the ball
- Global minimality of the degree-one Ginzburg-Landau vortex solution in the unit ball in dimensions n ≥ 2
- Optimal stability of Pál's isominwidth inequality for ball convex bodies in planes of constant curvature
- Adding Heavy-Ball Momentum to Distributed Constrained Optimization for Energy Resource Management Subject to Time-Delays and Quantization
- Explicit charge-conserving and modified energy-conserving PIC methods using the SAV approach
BibTeX
@misc{topaloglu2026minimality,
title = {{Minimality and stability of the ball for the charge-qubit energy}},
author = {Ihsan Topaloglu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27218},
eprint = {2610.27218},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27218},
}
RIS
TY - UNPB
TI - Minimality and stability of the ball for the charge-qubit energy
AU - Ihsan Topaloglu
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.27218
UR - https://arxiv.org/abs/2610.27218
AB - 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.
ER -