Closed-Form Solution to the Mori Formula and its Application

Abstract

The derivation of the closed-form solution to the generalized Langevin equation (Mori formula) is reviewed. We derive rigorous constraints for transport coefficients in the limit of low frequency and those obtained in the memory functional approach to the closed-form solution. We calculate the closed-form solution for the relaxation functions of the fluctuating force in a free two-band model to find a long-time tail of t^<-1> and the strongly colored quantum noise at T = 0.