On Fermionic walkers interacting with a correlated structured environment

We study the large-time behaviour of a sampleS consisting of an ensemble of fermionic walkers on a graph interactingwith a structured infinite reservoir of fermions E through an exchange of particles in preferred states. We describe the asymptotic state of S in terms the initial state of E, with especially simple formulae in the limit of small coupling strength. We also study the particle fluxes into the different parts of the reservoir.