Proof of the Closed-Form Solution to the Mori Formula for Transport Coefficients

Abstract

Three decades ago, the quantum Langevin-like equation (Mori formula) was used to reformulate the linear response theory (Kubo formula) in the continued fraction formalism.Since then, the Mori formula has often been used to evaluate transport coefficients, but only within the Born approximation. Very recently, a rigorous closed-form solution to the Mori formula for transport coefficients has been obtained. In the present study, we prove the equivalence of the closed-form solution to the Mori formula and the Kubo formula using the general relations between correlation functions and then comment on the Born approximation.