Lieb–Thirring inequality with semiclassical constant and gradient error term |
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Authors: | Phan Thành Nam |
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Institution: | Department of Mathematics and Statistics, Masaryk University, Kotlá?ská 2, 611 37 Brno, Czech Republic |
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Abstract: | In 1975, Lieb and Thirring derived a semiclassical lower bound on the kinetic energy for fermions, which agrees with the Thomas–Fermi approximation up to a constant factor. Whenever the optimal constant in their bound coincides with the semiclassical one is a long-standing open question. We prove an improved bound with the semiclassical constant and a gradient error term which is of lower order. |
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Keywords: | Lieb–Thirring inequality Semiclassical approximation Sharp constant Gradient error |
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