The exponent in the orthogonality catastrophe
نویسندگان
چکیده
We quantify the asymptotic vanishing of the ground-state overlap of two noninteracting Fermi gases in d -dimensional Euclidean space in the thermodynamic limit. Given two one-particle Schrödinger operators in nite-volume which di er 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 in terms of scattering theory and nd D 2k arcsin jTE=2jkHS, 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. Mathematics Subject Classi cation (2010). 35J10, 81Q10, 35P25.
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