Stochastic dynamics and bound states of heavy impurities in a Fermi bath

We investigate the dynamics of heavy impurities embedded in an ultracold Fermi gas by using a generalized Langevin equation. The latter - derived by means of influence functional theory - describes how the stochastic classical dynamics of the impurities and the quantum nature of the fermionic bath manifests in the emergent interaction between the impurities and in the viscosity tensor. By focusing on the two-impurity case, we predict the existence of bound states, in different conditions of coupling and temperature, whose lifetime can be analytically estimated. Our predictions should be testable using cold-gases platforms within current technology.