A New Estimate on the Two-Dimensional Indirect Coulomb Energy

TL;DR

This paper establishes a tighter lower bound on the two-dimensional indirect Coulomb energy in quantum mechanics, improving upon previous bounds by reducing the constant factor involved.

Contribution

It introduces a new universal lower bound on the Coulomb energy in 2D quantum systems, featuring a smaller constant than the existing Lieb--Solovej--Yngvason bound.

Findings

New lower bound with constant C≈5.90

Improved bound is an alternative to the Lieb--Solovej--Yngvason bound

Includes an additive gradient energy term

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.