Stability of a fermionic $N+1$ particle system with point interactions

TL;DR

This paper proves the stability of a fermionic N+1 particle system with point interactions when the additional particle's mass exceeds a critical value, with implications for the stability of the unitary Fermi gas.

Contribution

It establishes the critical mass ratio for stability, characterizes the Hamiltonian domain, and confirms Tan relations for this fermionic system.

Findings

System is stable if mass ratio exceeds critical value less than 1

Critical mass ratio is independent of particle number N

Tan relations hold for all wave functions in the Hamiltonian domain

Abstract

We prove that a system of $N$ fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical $m^*$. The value of $m^*$ is independent of $N$ and turns out to be less than $1$. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain.