Year: 1999
Type: preprint
Abstract: We prove a simple theorem on the overlap of the wavefunctions of a manybody system with and without a single impurity and show how, and under which conditions, this leads to the ``Orthogonality Catastrophe'' (OC) described by Anderson. A compact new derivation of the known result for the OC exponent in a free electron gas, $α=2 \sum_l(2l+1) (δ_l(ε_f)/π)^2 $ %$α= 2\sum_l [2l+1] (δ_l(ε_f)/π)^2$, is given. We also introduce a simple way of calculating core level photoemission (XPS) lineshapes from the finite size scaling of groundstate energies, reproducing and extending results previously derived using boundary conformal field theory. Different conditions under which the OC fails are discussed, and simple physical predictions for XPS lineshapes made in each case.
Source: arXiv (Cornell University)
Author: Shannon, Nic
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1532032095