# On Fermionic walkers interacting with a correlated structured environment

## TL;DR

This paper investigates the long-term dynamics of fermionic particles on a graph interacting with a structured fermionic environment, providing explicit formulas for asymptotic states and particle fluxes, especially at weak coupling.

## Contribution

It introduces a detailed analysis of fermionic walkers interacting with a correlated environment, deriving explicit asymptotic states and flux formulas, including in the weak coupling limit.

## Key findings

- Explicit formulas for the asymptotic state of the system.
- Characterization of particle fluxes into the reservoir.
- Simplified results in the small coupling limit.

## Abstract

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.