Quantum response theory is a cornerstone of statistical physics. However, the standard Kubo formalism is restricted to isolated equilibrium systems. We here generalize Kubo's results to open quantum systems in nonequilibrium steady states. We derive three different, but equivalent, forms of the quantum response function. We discuss for each of them the role of the noncommutativity of quantum operators and introduce a steady-state extension of the Kubo transformation. We show in particular that the equilibrium response vanishes for perturbations that commute with the unperturbed Hamiltonian, while the steady-state response does not, highlighting the profound difference between the two linear response theories.

• Received 10 December 2018

DOI:https://doi.org/10.1103/PhysRevResearch.1.033156

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society