Response theory for nonequilibrium steady-states of open quantum systems

TL;DR

This paper develops a response theory for open quantum systems in nonequilibrium steady states, revealing that their response to perturbations differs from closed systems and depends on the system-bath interaction regime.

Contribution

It introduces a novel response framework for open quantum systems within the Lindblad formalism, extending beyond traditional fluctuation-dissipation relations.

Findings

Response not simply related to system correlation functions.

Perturbative expansion valid in certain regimes with additional environmental forces.

Singular response arises outside limiting regimes, requiring microscopic Hamiltonian analysis.

Abstract

We introduce a response theory for open quantum systems within nonequilibrium steady-states subject to a Hamiltonian perturbation. Working in the weak system-bath coupling regime, our results are derived within the Lindblad-Gorini-Kossakowski-Sudarshan formalism. We find that the response of the system to a small perturbation is not simply related to a correlation function within the system, unlike traditional linear response theory in closed systems or expectations from the fluctuation-dissipation theorem. In limiting cases, when the perturbation is small relative to the coupling to the surroundings or when it does not lead to a change of the eigenstructure of the system, a perturbative expansion exists where the response function is related to a sum of a system correlation functions and additional forces induced by the surroundings. Away from these limiting regimes however, the secular approximation results in a singular response that cannot be captured within the traditional approach, but can be described by reverting to a microscopic Hamiltonian description. These findings are illustrated by explicit calculations in coupled qubits and anharmonic oscillators in contact with bosonic baths at different temperatures.