Effective pair interaction between impurity particles induced by a dense Fermi gas

TL;DR

This paper investigates how impurity particles in a dense Fermi gas develop an effective attractive interaction among themselves, emerging from the quantum fluctuations of the surrounding fermions in high-density regimes.

Contribution

It demonstrates that in the high-density limit, impurity particles effectively decouple from the Fermi gas and interact via an induced attractive pair potential.

Findings

Impurities decouple from the Fermi gas at high density.

An effective attractive interaction between impurities is induced by Fermi gas fluctuations.

The results are valid in the large-volume and high-density limits with specific coupling scaling.

Abstract

We study the dynamics of a small number of impurity particles coupled to the ideal Fermi gas in a $d$-dimensional box. The impurities interact with the fermions via a two-body potential $\lambda v(x)$ where $\lambda$ is a coupling constant and $v(x)$ for instance a screened Coulomb potential. After taking the large-volume limit at positive Fermi momentum $k_F$ we consider the regime of high density of the fermions, that is, $k_F$ large compared to one. For coupling constants that scale like $\lambda^2 \sim k_F^{(2-d)}$ we show that the impurity particles effectively decouple from the fermions but evolve with an attractive pair interaction among each other which is induced by fluctuations in the Fermi gas.