The Lieb-Thirring inequality for interacting systems in strong-coupling limit
Mathematical Physics
2021-03-31 v3 Analysis of PDEs
math.MP
Spectral Theory
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.
Cite
@article{arxiv.2006.04729,
title = {The Lieb-Thirring inequality for interacting systems in strong-coupling limit},
author = {Kevin Kögler and Phan Thành Nam},
journal= {arXiv preprint arXiv:2006.04729},
year = {2021}
}
Comments
Final version to appear in Arch. Ration. Mech. Anal