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. 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.

48 pages; revised version including a new result (Thm. 2.6); to appear in Duke Mathematical Journal

References in corpus (2)

• A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case
• Energy Cost to Make a Hole in the Fermi Sea

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