Improved Lieb-Oxford bound on the indirect and exchange energies

Autor: Lewin, Mathieu, Lieb, Elliott H., Seiringer, Robert
Rok vydání: 2022
Předmět:
Zdroj: Lett. Math. Phys. 112:92 (2022)
Druh dokumentu: Working Paper
DOI: 10.1007/s11005-022-01584-5
Popis: The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree-Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy.
Comment: Final version to appear in Lett. Math. Phys. This article belongs to the themed collection: "Mathematical Physics and Numerical Simulation of Many-Particle Systems"; V. Bach and L. Delle Site (eds.)
Databáze: arXiv
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