PreprintarXiv licencearXiv
Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region
Abstract
We study the asymptotic behavior of positive ground states of N-particle atomic Coulomb Hamiltonians in a two-cluster region. For the N-particle ground state ψ, its one-particle density ρ, and (N−1)-particle ground state ϕ, we show that for 0<α<1, as |xN|→∞, ψ(x1,…,xN)/√(ρ(xN))= ϕ(x1,…,xN−1)+O(|xN|−2+α ln |xN|) uniformly in the region |xi|≤ |xN|α. In the region |xi|≤ R0ln |xN|, the convergence rate is O(|xN|−2 (ln |xN|)2). We also establish an O(|xN|−2) bound on the squared L2 error. These results hold both below the essential spectrum and at threshold.
Related
- Exact SU(N) symmetry resolution of bosonic Hubbard models: general boson-fermion mappings and flat-band singlet-cluster states
- Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians
- Quantum cluster structures on bosonic extensions
- Cluster Algebras for Bosonic Plethysm
- Ground state solutions and asymptotics for discrete Kirchhoff problems
BibTeX
@misc{goto2026asymptotics,
title = {{Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region}},
author = {Yukimi Goto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08257},
eprint = {2609.08257},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08257},
}
RIS
TY - UNPB
TI - Asymptotics of Ground States for Helium-Like and Bosonic Atoms in a Two-Cluster Region
AU - Yukimi Goto
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08257
UR - https://arxiv.org/abs/2609.08257
AB - We study the asymptotic behavior of positive ground states of N-particle atomic Coulomb Hamiltonians in a two-cluster region. For the N-particle ground state ψ, its one-particle density ρ, and (N−1)-particle ground state ϕ, we show that for 0<α<1, as |x_N|→∞, ψ(x_1,…,x_N)/√(ρ(x_N))= ϕ(x_1,…,x_N−1)+O(|x_N|^−2+α ln |x_N|) uniformly in the region |x_i|≤ |x_N|^α. In the region |x_i|≤ R_0ln |x_N|, the convergence rate is O(|x_N|^−2 (ln |x_N|)^2). We also establish an O(|x_N|^−2) bound on the squared L^2 error. These results hold both below the essential spectrum and at threshold.
ER -