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Kogler, Kevin and Nam, Phan Thanh (2021): The Lieb-Thirring Inequality for Interacting Systems in Strong-Coupling Limit. In: Archive for Rational Mechanics and Analysis, Vol. 240, No. 3: pp. 1169-1202

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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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