The exponent in the orthogonality catastrophe for Fermi gases

Gebert, Martin; Küttler, Heinrich; Müller, Peter und Otte, Peter (2016): The exponent in the orthogonality catastrophe for Fermi gases. In: Journal of Spectral Theory, Bd. 6, Nr. 3: S. 643-683

Abstract

We quantify the asymptotic vanishing of the ground-state overlap of two non-interacting Fermi gases in d-dimensional Euclidean space in the thermodynamic limit. Given two one-particle Schrödinger operators in finite-volume which differ by a compactly supported bounded potential, we prove a power-law upper bound on the ground-state overlap of the corresponding non-interacting N-Fermion systems. We interpret the decay exponent γ in terms of scattering theory and find γ=π−2∥arcsin|TE/2|∥2HS, where TE is the transition matrix at the Fermi energy E. This exponent reduces to the one predicted by Anderson [Phys. Rev. 164, 352–359 (1967)] for the exact asymptotics in the special case of a repulsive point-like perturbation.

• Dokumententyp: Zeitschriftenartikel
• Publikationsform: Publisher's Version
• Keywords: Schrödinger operators; Anderson orthogonality; spectral correlations; scattering theory
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1664-039X
• Allianz-/Nationallizenz: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
• Sprache: Englisch