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Uniqueness, Nondegeneracy, and Asymptotic Expansions of Ground States for the Dirac-Coulomb System
Abstract
We study ground states of the following Dirac-Coulomb system πcucβ (absxβ1β absuc2)uc=Οcuc, under the constraint norm[L2]uc2=1.For sufficiently large c, we prove uniqueness of ground states modulo translations, phase transformations and spinorial rotations, and determine the kernel of the linearized operator at ground state. We also obtain asymptotic expansions of ground state in the nonrelativistic limit regime.
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BibTeX
@misc{chen2026uniqueness,
title = {{Uniqueness, Nondegeneracy, and Asymptotic Expansions of Ground States for the Dirac-Coulomb System}},
author = {Pan Chen and Qi Guo and Xiaoyu Zeng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22953},
eprint = {2609.22953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22953},
}
RIS
TY - UNPB
TI - Uniqueness, Nondegeneracy, and Asymptotic Expansions of Ground States for the Dirac-Coulomb System
AU - Pan Chen
AU - Qi Guo
AU - Xiaoyu Zeng
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22953
UR - https://arxiv.org/abs/2609.22953
AB - We study ground states of the following Dirac-Coulomb system π_cu_cβ (absx^β1β absu_c^2)u_c=Ο_cu_c, under the constraint norm[L^2]u_c^2=1.For sufficiently large c, we prove uniqueness of ground states modulo translations, phase transformations and spinorial rotations, and determine the kernel of the linearized operator at ground state. We also obtain asymptotic expansions of ground state in the nonrelativistic limit regime.
ER -