A positive density analogue of the Lieb-Thirring inequality

Details A positive density analogue of the Lieb-Thirring inequality A positive density analogue of the Lieb-Thirring inequality

2011-08-22

arxiv.org/abs/1108.4246v1

Physics

Mathematical Physics

Scientific paper

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.

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