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.
arXiv commentFinal version to appear in Arch. Ration. Mech. Anal
References in corpus (14)
- A simple proof of Hardy-Lieb-Thirring inequalities
- The Local Density Approximation in Density Functional Theory
- Hardy and Lieb-Thirring inequalities for anyons
- Local exclusion principle for identical particles obeying intermediate and fractional statistics
- Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics
- Exclusion bounds for extended anyons
- Fractional Hardy-Lieb-Thirring and related inequalities for interacting systems
- The Lieb-Thirring inequality revisited
- Lieb-Thirring Bounds for Interacting Bose Gases
- Lieb-Thirring inequality with semiclassical constant and gradient error term
- Lieb-Thirring Inequality for a Model of Particles with Point Interactions
- The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities
- Fermionic behavior of ideal anyons
- Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics