Energy lower bound for the unitary N+1 fermionic model

TL;DR

This paper investigates the stability of a system with N fermions interacting with a different particle at infinite scattering length, providing a simplified proof of a known stability condition based on mass ratio.

Contribution

It offers a more direct and simplified proof of the stability condition for the unitary N+1 fermionic model, extending previous results.

Findings

Established a lower energy bound for the model

Provided a simplified proof of the stability condition

Confirmed the dependence on mass ratio for stability

Abstract

We consider the stability problem for a unitary N+1 fermionic model, i.e., a system of $N$ identical fermions interacting via zero-range interactions with a different particle, in the case of infinite two-body scattering length. We present a slightly more direct and simplified proof of a recent result obtained in \cite{CDFMT}, where a sufficient stability condition is proved under a suitable assumption on the mass ratio.