A positive density analogue of the Lieb-Thirring inequality
Mathematical Physics
2019-12-19 v2 Quantum Gases
math.MP
Spectral Theory
Abstract
The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schr\"odinger operator in terms of an norm of the potential. This is dual to a bound on the -norms of a system of orthonormal functions. Here we extend these to analogous inequalities for perturbations of the Fermi sea of non-interacting particles, i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials.
Keywords
Cite
@article{arxiv.1108.4246,
title = {A positive density analogue of the Lieb-Thirring inequality},
author = {Rupert L. Frank and Mathieu Lewin and Elliott H. Lieb and Robert Seiringer},
journal= {arXiv preprint arXiv:1108.4246},
year = {2019}
}
Comments
48 pages; revised version including a new result (Thm. 2.6); to appear in Duke Mathematical Journal