A theory of selective reflection and transmission is developed for a system consisting of a thin layer of a dilute atomic vapor sandwiched between two transparent solids with parallel interfaces. Strong effects of spatial dispersion due to the atomic motion and electronic quenching on gas-solid interfaces are accounted for. It is shown that both even and odd Doppler-free resonances may occur in selective reflection, depending upon the thickness of the vapor layer. It is also found that the amplitude of selective reflection is a result of the interference between reflections from the two boundaries of the vaporsolid interfaces and, hence, may be greatly enhanced under certain conditions.

The equation of motion for nonequilibrium Green functions is derived within the framework of the Schwinger and Keldysh formalism of perturbation expansion. For nonequilibrium distribution Green functions, the equation of motion derived from quantum mechanics contains undefined singularities, whose explicit form depends on the specific initial or boundary condition. In the present work, the exact expression of singular terms is found in the equation of motion from the time-looped perturbation theory in which the adiabatic initial condition is implied. Unlike the usual Dyson perturbation formalism or the well known Kadanoff-Baym equation of motion, our resulting equation can be adopted directly for calculations without the graphical analysis, which depends on the specific form of the Hamiltonian. On the basis of this equation of motion, the procedure of a nonperturbative solution is outlined and potential applications are briefly discussed.

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The method of the retarded-Green s-function equation of motion is applied to investigate the spin-wave spectrum and other properties of two-sublattice Heisenberg ferrimagnets. The algebraic procedure is greatly simplified by introducing the matrix equation for the ferrimagnet for both NaCl and CsC1 structures. %'e find that the spin-wave spectrum breaks into acoustical and optical branches as expected. The mean spin values of individual sublattices are calculated numerically for different single-particle spin values. It is seen that in the special case of an antiferromagnet, our results agree completely with existing work.