The Lieb-Thirring inequality for interacting systems in strong-coupling limit
arXiv:2006.04729 · doi:10.1007/s00205-021-01633-8
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.
Final version to appear in Arch. Ration. Mech. Anal