The exponent in the orthogonality catastrophe for Fermi gases

Gebert, Martin; Küttler, Heinrich; Müller, Peter; Otte, Peter (2016): The exponent in the orthogonality catastrophe for Fermi gases. In: Journal of Spectral Theory, Vol. 6, No. 3: pp. 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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Keywords: Schrödinger operators; Anderson orthogonality; spectral correlations; scattering theory
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1664-039X
• Alliance/National Licence: This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
• Language: English