Asymmetrical Hubbard model in the generating functional technique: spectral functions in the Falikov-Kimbal limit

In terms of the dynamic mean field one studied the state densities of the spectrum fermion and boson branches of the Hubbard asymmetrical model applied to describe a strongly correlated varietal system of the Fermi-particles (electrons). To solve the effective single-point problem one extends the approximated analytical approach based on the method of the generating functional. The mentioned procedure enables to obtain the nonreducible part (mass operator) of the Green function of the particles in the form of the coherent potential power formal expansion. Within the first order the pattern reproduces the Hubbard-III so-called generalized approximation. To improve it one elaborates the self-congruent procedure to calculate the Green both fermion and boson functions. Within the Falikov-Kimball limit of the Hubbard asymmetrical model one derived the spectral densities of the states of both branches. One studied variation of their form depending on the particle temperature and concentration. One determined the applicability limits of the Hubbard-III generalized approximation