On quasi-particle descriptions of many particle systems

Quasi-particle descriptions of thermal or weakly turbulent fluctuations in classical many particle systems may be derived with the aid of a complete set of eigenmodes. For a Maxwell-Vlasov electron plasma, the latter comprise a set of continuous and discrete modes, the continuum modes being dressed single-particle excitations with real eignvalues. Fluctuation field correlations can be represented in terms of either the continuous eigenmodes or discrete quasi-modes; the latter characterize collective waves corresponding to complex quasi-eigenvalues (Landau poles)on the unphysical sheet of the complex frequency Plane. Quasi-mode representations of the dynamics of weakly correlated fluctuations can be interpreted in terms of quasi-particles moving in their phase space along trajectories determined by dispersion relations characteristic of quasi-mode "energy." The quasi-particle density in phase space is determined by the amplitude correlation spectrum of the quasimodes.