A positive density analogue of the Lieb-Thirring inequality
  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. 
Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
math-ph cond-mat.quant-gas math.MP math.SP