A New Estimate on the Two-Dimensional Indirect Coulomb Energy

Details A New Estimate on the Two-Dimensional Indirect Coulomb Energy A New Estimate on the Two-Dimensional Indirect Coulomb Energy

2011-06-28

arxiv.org/abs/1106.5772v5

Physics

Mathematical Physics

Scientific paper

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.

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