%0 Journal Article
%T A positive density analogue of the Lieb-Thirring inequality
%A Rupert L. Frank
%A Mathieu Lewin
%A Elliott H. Lieb
%A Robert Seiringer
%J Physics
%D 2011
%I arXiv
%X The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schr\"odinger operator in terms of an $L^p$ norm of the potential. This is dual to a bound on the $H^1$-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.
%U http://arxiv.org/abs/1108.4246v2