Fermionic walkers driven out of equilibrium

TL;DR

This paper analyzes the non-Hamiltonian dynamics of a fermionic quantum system coupled to reservoirs, deriving explicit formulas for the asymptotic state, fermion fluxes, and entropy production rate, especially at weak coupling.

Contribution

It provides explicit leading-order formulas for the asymptotic behavior and fluxes in a fermionic system with translation symmetry, extending understanding of non-Hamiltonian quantum dynamics.

Findings

Explicit formulas for asymptotic states and fluxes

Leading order expansion in coupling strength

Quantitative analysis of entropy production rate

Abstract

We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic state, mean fluxes of fermions into the different reservoirs, as well as the mean entropy production rate of the dynamics. Formulas are explicitly expanded to leading order in the strength of the coupling to the reservoirs.