New theory of nonlinear optical conductivity for an electron-phonon system

A new theory is presented for the nonlinear optical conductivity of a system of electrons interacting with phonons. The difference between the present theory and the previous ones lies in the projectors; thus, the results are somewhat different from one other. The present result includes the electron and phonon distribution functions properly and provides general interpretations of the phonon emissions and absorptions in all electron transition processes. Satisfactory approval of the theory, however, can be made only by comparison, which is impossible at present.