354 research outputs found
The exponent in the orthogonality catastrophe for Fermi gases
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 Schr\"odinger 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 -particle 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.Comment: Version as to appear in J. Spectr. Theory, References update
Oligoclonality of serum-antibodies to exocrine pancreas in Crohn´s disease and to intestinal goblet cells in ulcerative colitis
A Szeg\H{o} Limit Theorem Related to the Hilbert Matrix
The Szeg\H{o} limit theorem by Fedele and Gebert for matrices of the type
identity minus Hankel matrix is proved for the special case
where is the -Hilbert matrix, , and . The proof
uses operator theoretic tools and a reduction to the classical Kac--Akhiezer
theorem for the Carleman operator. Thereby, the validity of the theorem for
this special Hankel matrix can be extended from to
. The bound on the correction term is
improved to instead of for . The limit case is derived directly from the asymptotics
for general
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