Impurities in Schrödinger field theories and s-wave resonance

Abstract

We study point impurities in non-relativistic quantum field theories, with a focus on scale-invariant fixed points. We establish the framework of conformal defects in Schrödinger field theories and their correspondence to many-body states in a harmonic trap. We discuss a multi-critical quantization of the one-body wave function induced by an impurity, with examples of free and unitary Fermi gases. Our results can potentially be tested in experimental setups.

Comments: 14 pages, 6 figures; typo corrected in V2