Impurities in Schr\"{o}dinger field theories and s-wave resonance

TL;DR

This paper develops a framework for understanding point impurities in non-relativistic Schr"{o}dinger field theories, linking conformal defects to many-body states, with potential experimental applications.

Contribution

It introduces a conformal defect framework in Schr"{o}dinger theories and explores impurity effects on many-body states, including multi-critical quantization.

Findings

Framework for conformal defects in Schr"{o}dinger theories

Connection between defects and many-body states in traps

Impurity effects in free and unitary Fermi gases

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 Schr\"{o}dinger 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.