Impurity with a resonance in the vicinity of the Fermi energy

We study an impurity with a resonance level whose position coincides with the Fermi energy of the surrounding Fermi gas. An impurity causes a rapid variation of the scattering phase shift for fermions at the Fermi surface, introducing a new characteristic length scale into the problem. We investigate manifestations of this length scale in the self-energy of the impurity and in the density of the bath. Our calculations reveal a model-independent deformation of the density of the Fermi gas, which is determined by the width of the resonance. To provide a broader picture, we investigate time evolution of the density in quench dynamics, and study the behavior of the system at finite temperatures. Finally, we briefly discuss implications of our findings for the Fermi-polaron problem.

Automated summary

We study the impact of an impurity with a resonance level on a surrounding Fermi gas. Our findings show that the impurity causes changes in its self-energy and the density of the gas, leading to a model-independent deformation of the Fermi gas density. Additionally, the study investigates the time evolution of the density in quench dynamics and the behavior of the system at finite temperatures.