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The Lieb-Thirring inequality for interacting systems in strong-coupling limit (2006.04729v3)
Published 8 Jun 2020 in math-ph, math.AP, math.MP, and math.SP
Abstract: We consider an analogue of the Lieb-Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb-Thirring constant converges to the optimal constant of the one-body Gagliardo-Nirenberg interpolation inequality without interaction.
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