Non-equilibrium quantum chains under multi-site Lindblad baths

TL;DR

This paper analyzes a quantum XX chain coupled to multi-site heat reservoirs using Lindblad dissipators, deriving analytical steady-state properties, currents, and Onsager coefficients, revealing significant differences from single-site baths and confirming Onsager relations in weak coupling.

Contribution

It provides the first analytical formulas for steady-state properties of a quantum chain with multi-site Lindblad baths, highlighting the impact of bath coupling strength.

Findings

Currents follow Landauer's formula structure.

Steady-state properties differ from single-site bath models.

Onsager reciprocal relations hold in the weak coupling regime.

Abstract

We study a quantum XX chain coupled to two heat reservoirs that act on multiple-sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formulas for all steady-state properties of the system. We compute both the particle/magnetization current and the energy current, both of which are found to have the structure of Landauer's formula. We also obtain exact formulas for the Onsager coefficients. All properties are found to differ substantially from those of a single-site bath. In particular, we find a strong dependence on the intensity of the bath couplings. In the weak coupling regime, we show that the Onsager reciprocal relations are satisfied.