Impurity in Schrödinger field theories and s-wave resonance

We discuss point impurities in scale-invariant critical systems, focusing on non-relativistic physics. We established the conformal defect formalism and studied the renormalization flow between various fixed points of the impurity. As an example, we will extensively discuss impurities in free and unitary Fermi gases, and several analytical results are obtained. Our work also applies to superfluids, neutron scattering, and many-body wave functions in harmonic traps.