Duke Mathematical Journal

A positive density analogue of the Lieb–Thirring inequality

Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, and Robert Seiringer

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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).

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Duke Math. J. Volume 162, Number 3 (2013), 435-495.

First available in Project Euclid: 14 February 2013

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Zentralblatt MATH identifier

Primary: 35P15: Estimation of eigenvalues, upper and lower bounds
Secondary: 35J10: Schrödinger operator [See also 35Pxx] 81Q20: Semiclassical techniques, including WKB and Maslov methods 35Q40: PDEs in connection with quantum mechanics


Frank, Rupert L.; Lewin, Mathieu; Lieb, Elliott H.; Seiringer, Robert. A positive density analogue of the Lieb–Thirring inequality. Duke Math. J. 162 (2013), no. 3, 435--495. doi:10.1215/00127094-2019477. https://projecteuclid.org/euclid.dmj/1360874852.

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