Stationarity as a One-Mode Constraint on Quantum Correlation
Abstract
A stationary scalar correlation energy admits an exact one-mode terminal representation even when the microscopic correlated return is strongly multimode. We test predictive realizations built from specified stationary information carriers in two complementary two-electron systems with the same Coulomb repulsion but different confinement: He-like ions and harmonium (Hooke's atom). For the Coulomb sequence, canonical RHF supplies the symmetry-faithful information carrier. The repeated same-mode return gives a He correlation error of +0.1164 mEh and no more than $0.0157$ mEh for Li+--Ar16+; H- is nevertheless bound and 93.3% of its conventional correlation energy is recovered even though the RHF carrier is qualitatively strained. The dimensionless confinement factor RCC=DCC/Z tends to $1.092394$. For harmonic confinement, an independently constructed response-compressed one-mode return gives RH=DH/√ω; for ω≥0.1 it agrees with reference-inferred values within 0.21% and tends to the literature high-density limit $1.309283$. Cioslowski and Pernal locate the qualitative crossover to the radially localized strongly correlated harmonium regime at ωcrit≃0.04012, below the quantitative domain used here. The H- endpoint and ωcrit are therefore complementary carrier-validity boundaries: they limit the predictive realization, not exact terminal one-mode representability. A broad helium Bethe--Goldstone spectrum confirms that this terminal statement is not microscopic one-pole dynamics.
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BibTeX
@misc{panas2026stationarity,
title = {{Stationarity as a One-Mode Constraint on Quantum Correlation}},
author = {Itai Panas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02090},
eprint = {2610.02090},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02090},
}
RIS
TY - UNPB
TI - Stationarity as a One-Mode Constraint on Quantum Correlation
AU - Itai Panas
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.02090
UR - https://arxiv.org/abs/2610.02090
AB - A stationary scalar correlation energy admits an exact one-mode terminal representation even when the microscopic correlated return is strongly multimode. We test predictive realizations built from specified stationary information carriers in two complementary two-electron systems with the same Coulomb repulsion but different confinement: He-like ions and harmonium (Hooke's atom). For the Coulomb sequence, canonical RHF supplies the symmetry-faithful information carrier. The repeated same-mode return gives a He correlation error of +0.1164 mE_h and no more than $0.0157$ mE_h for Li^+--Ar^16+; H^- is nevertheless bound and 93.3% of its conventional correlation energy is recovered even though the RHF carrier is qualitatively strained. The dimensionless confinement factor R_CC=D_CC/Z tends to $1.092394$. For harmonic confinement, an independently constructed response-compressed one-mode return gives R_H=D_H/√ω; for ω≥0.1 it agrees with reference-inferred values within 0.21% and tends to the literature high-density limit $1.309283$. Cioslowski and Pernal locate the qualitative crossover to the radially localized strongly correlated harmonium regime at ω_crit≃0.04012, below the quantitative domain used here. The H^- endpoint and ω_crit are therefore complementary carrier-validity boundaries: they limit the predictive realization, not exact terminal one-mode representability. A broad helium Bethe--Goldstone spectrum confirms that this terminal statement is not microscopic one-pole dynamics.
ER -