A New Estimate on the Two-Dimensional Indirect Coulomb Energy
Mathematical Physics
2015-05-28 v5 math.MP
Quantum Physics
Abstract
We prove a new lower bound on the indirect Coulomb energy in two dimensional quantum mechanics in terms of the single particle density of the system. The new universal lower bound is an alternative to the Lieb--Solovej--Yngvason bound with a smaller constant, C=(4/3)^{3/2}\sqrt{5 \pi -1} \approx 5.90 < C_{LSY}= 192\sqrt{2 \pi} \approx 481.27, which also involves an additive gradient energy term of the single particle density.
Keywords
Cite
@article{arxiv.1106.5772,
title = {A New Estimate on the Two-Dimensional Indirect Coulomb Energy},
author = {Rafael D. Benguria and Pablo Gallegos and Matej Tusek},
journal= {arXiv preprint arXiv:1106.5772},
year = {2015}
}