Non-additive dissipation in open quantum networks out of equilibrium

TL;DR

This paper analyzes a simple quantum network with two fermionic modes coupled to separate thermal reservoirs, revealing non-additive effects in the steady-state dynamics due to interference terms.

Contribution

It demonstrates that the generator of the master equation is non-additive and identifies interference effects that generate coherences in the energy basis.

Findings

Non-additivity persists even with weak, wide-band reservoirs.

Interference terms induce coherences in the energy eigenbasis.

Steady-state particle currents are linked to non-additive dynamics.

Abstract

We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.