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Gebert, Martin; Küttler, Heinrich; Müller, Peter and Otte, Peter (2016): The exponent in the orthogonality catastrophe for Fermi gases. In: Journal of Spectral Theory, Vol. 6, No. 3: pp. 643-683 [PDF, 430kB]

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.

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