Theory of conductivity and scattering factor-functions in quasi two-dimensional system based on ensemble-average projection scheme

In the present work, utilizing the equilibrium average projection scheme (EAPS), we will introduce ways to obtain the conductivity formulas which include the scattering factor-function in quasi two-dimensional system. The confinement potential shall be chosen to be a parabolic one. We expand propagators via series-expansion projected Liouville equilibrium operators and expand the propagators via series expansions projected diagonal Liouville operators. We find some useful relations to calculate the scattering factor-function.