Orthogonality catastrophe in Coulomb systems

The orthogonality catastrophe (OC) problem is considered solved for fifty years. It has important consequences for numerous dynamic phenomena in fermionic systems, including Kondo effect, X-ray spectroscopy, and quantum diffusion of impurities, and is often used in the context of metals. However, the key assumptions on which the known solution is based---impurity potentials with finite cross-section and non-interacting fermions---are both fundamentally invalid for problems involving charged particles in metals. As far as we know, the OC problem for "all Coulomb" case has never been addressed systematically due to its apparent complexity, leaving it unsolved for the most relevant practical applications. In this work we include effects of dynamic screening of long-range Coulomb potentials in a systematic way and establish that gapped plasmon modes reduce but do not eliminate the power-law in time decay of the overlap integral.