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

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