We study the large-time behaviour of a sample $\mathcal{ S}$ consisting of an ensemble of fermionic walkers on a graph interacting with a structured infinite reservoir of fermions $\mathcal{ E}$ through an exchange of particles in preferred states. We describe the asymptotic state of $\mathcal{ S}$ in terms the initial state of $\mathcal{ E}$, with especially simple formulae in the limit of small coupling strength. We also study the particle fluxes into the different parts of the reservoir.
Categories: math-ph math.MP quant-ph