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, \({C = (4/3)^{3/2} \sqrt{5 \pi -1} \approx 5.90 < C_{\rm LSY} = 192 \sqrt{2 \pi} \approx 481.27}\), which also involves an additive gradient energy term of the single particle density.
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Communicated by Claude Alain Pillet.
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Benguria, R.D., Gallegos, P. & Tušek, M. A New Estimate on the Two-Dimensional Indirect Coulomb Energy. Ann. Henri Poincaré 13, 1733–1744 (2012). https://doi.org/10.1007/s00023-012-0176-x
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DOI: https://doi.org/10.1007/s00023-012-0176-x