The Kubo formula expresses a linear response through an equilibrium correlation function. For a perturbation and observable , one convention gives , withThe step function enforces causality, and the commutator records the quantum response.
The sign depends on the declared perturbing-Hamiltonian convention. Applying the framework to currents or polarization relates transport coefficients to fluctuations in an unperturbed system, forming a foundation of linear response theory and the fluctuation-dissipation theorem.[ref]
Statistical-Mechanical Theory of Irreversible Processes. I by Ryogo Kubo. 1957 general response, relaxation and correlation framework
