Kubo and Zubarev Formulations of Response Theory

Eugen Fick, Günter Sauermann

Masuo Suzuki

The quantum derivatives of e−A, A−1 and log A, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator A in a Hilbert space. Using the quantum analysis based on these quantum derivatives, a basic equation for the entropy operator in nonequilibrium systems is derived, and Zubarev's theory is extended to infinite order with respect to a perturbation. Using the first-order term of this general perturbational expansion of the entropy operator, Kubo's linear response is rederived and expressed in terms of the inner derivation for the relevant Hamiltonian . Some remarks on the conductivity σ(ω) are given.

Michael Rudolf Vogl

Michael Konopik, Eric Lutz

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.