Fluctuation-Dissipation Relation for Open Quantum Systems in Nonequilibrium Steady State

TL;DR

This paper investigates the fluctuation-dissipation relation in a nonequilibrium steady state of a quantum harmonic chain connected to thermal baths at different temperatures, revealing an additional bias current term related to heat flow.

Contribution

It extends the fluctuation-dissipation relation to nonequilibrium steady states in quantum systems, identifying a bias current term linked to temperature differences and heat flow.

Findings

The conventional FDR does not hold in NESS for the quantum chain.

An additional bias current term appears, depending on temperature difference and coupling.

The bias current relates to steady heat flow between baths.

Abstract

Continuing our work on the nature and existence of fluctuation-dissipation relations (FDR) in linear and nonlinear open quantum systems [1-3], here we consider such relations when a linear system is in a nonequilibrium steady state (NESS). With the model of two-oscillators (considered as a short harmonic chain with the two ends) each connected to a thermal bath of different temperatures we find that when the chain is fully relaxed due to interaction with the baths, the relation that connects the noise kernel and the imaginary part of the dissipation kernel of the chain in one bath does not assume the conventional form for the FDR in equilibrium cases. There exists an additional term we call the `bias current' that depends on the difference of the bath's initial temperatures and the inter-oscillator coupling strength. We further show that this term is related to the steady heat flow between the two baths when the system is in NESS. The ability to know the real-time development of the inter-heat exchange (between the baths and the end-oscillators) and the intra-heat transfer (within the chain) and their dependence on the parameters in the system offers possibilities for quantifiable control and in the design of quantum heat engines or thermal devices.