# The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit

@article{Kgler2020TheLI, title={The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit}, author={Kevin K{\"o}gler and Phan Th{\`a}nh Nam}, journal={arXiv: Mathematical Physics}, year={2020} }

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.

## 2 Citations

### Direct methods to Lieb-Thirring kinetic inequalities

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- 2020

We review some recent progress on Lieb-Thirring inequalities, focusing on direct methods to kinetic estimates for orthonormal functions and applications for many-body quantum systems.

### A proof of the Lieb-Thirring inequality via the Besicovitch covering lemma

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- 2022

. We give a proof of the Lieb–Thirring inequality on the kinetic energy of orthonormal functions by using a microlocal technique, in which the uncertainty and exclusion principles are combined…

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