A positive density analogue of the Lieb–Thirring inequality

Abstract

The Lieb–Thirring inequalities give a bound on the negative eigenvalues of a Schrödinger operator in terms of an $L^p$-norm of the potential. These are dual to bounds on the $H^1$-norms of a system of orthonormal functions. Here we extend these bounds to analogous inequalities for perturbations of the Fermi sea of noninteracting particles (i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials).