Year: 2026
Type: preprint
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 $|x_N|\to\infty$, $ψ(x_1,\dots,x_N)/\sqrt{ρ(x_N)}= ϕ(x_1,\dots,x_{N-1})+O(|x_N|^{-2+α} \ln |x_N|)$ uniformly in the region $|x_i|\le |x_N|^α$. In the region $|x_i|\le R_0\ln |x_N|$, 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.
Source: arXiv (Cornell University)
Author: Goto, Yukimi
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
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OpenAlex ID: W7212012291