  The spectrum structures and behaviors of the Vlasov-Maxwell-Boltzmann (VMB)
systems for both two species and one species are studied in this paper. The
analysis shows the effect of the Lorentz force induced by the electro-magnetic
field leads to some different structure of spectrum from the classical
Boltzmann equation and the closely related Vlasov-Poisson-Boltzmann system. And
the significant difference between the two-species VMB model and one-species
VMB model are given. The structure in high frequency illustrates the hyperbolic
structure of the Maxwell equation. Furthermore, the long time behaviors and the
optimal convergence rates to the equilibrium of the Vlasov-Maxwell-Boltzmann
systems for both two species and one species are established based on the
spectrum analysis, and in particular the phenomena of the electric field
dominating and magnetic field dominating are observed for the one-species
Vlasov-Maxwell-Boltzmann system.
