Comments on the Mori Formula for Transport Coefficients

Abstract

Three decades ago, the quantum Langevin equation (Mori formula) wasused to reformulate the linear response theory (Kubo formula). Sincethen, the Mori formula has often been used to evaluate transportcoefficients, but only within the Born approximation. In the presentstudy, we obtain a rigorous expression for the transport coefficientsas a series expansion in terms of the projection operator. We thenevaluate the optical conductivity for a free electron system withimpurity scattering in order to discuss the mutual consistency betweenthe Mori formula and the Kubo formula.