Energy contribution of a point interacting impurity in a Fermi gas

TL;DR

This paper establishes a bound on the energy change in a Fermi gas caused by a point-interacting impurity, depending on density and scattering length, valid for certain mass ratios.

Contribution

It provides a new energy bound for a Fermi gas with an impurity, extending understanding of impurity effects in quantum many-body systems.

Findings

Energy change bound depends on density and scattering length

Bound is independent of the number of particles N

Applicable for impurity-to-particle mass ratio above a critical value

Abstract

We give a bound on the ground state energy of a system of $N$ non-interacting fermions in a three dimensional cubic box interacting with an impurity particle via point interactions. We show that the change in energy compared to the system in the absence of the impurity is bounded in terms of the gas density and the scattering length of the interaction, independently of $N$. Our bound holds as long as the ratio of the mass of the impurity to the one of the gas particles is larger than a critical value $m_c\approx 0.36$, which is the same regime for which we recently showed stability of the system.