Derivation of line shape function in the optical conductivity by a new diagram method

Abstract

A new diagram method to derive line shape function in the optical conductivity formula is introduced and the result obtained applying the method to an electron-phonon system is compared with that derived using the projection-reduction method. The result satisfies the population criterion, which states that the distribution functions for electrons and phonons should be combined in multiplicative forms, and gives physical intuition to quantum dynamics of electrons in a solid. This method can be called the "KC diagram" method because it originates from the proper application of the Kang-Choi reduction identity and a state-dependent projection operator.