We quantify the asymptotic vanishing of the ground-state overlap of two non-interacting Fermi gases in -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 -Fermion systems. We interpret the decay exponent in terms of scattering theory and find , where is the transition matrix at the Fermi energy . 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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Martin Gebert, Heinrich Küttler, Peter Müller, Peter Otte, The exponent in the orthogonality catastrophe for Fermi gases. J. Spectr. Theory 6 (2016), no. 3, pp. 643–683DOI 10.4171/JST/135