Transport Theory and Collective Modes. I. The Case of Moderately Dense Gases

Abstract

The complex spectral representation of the Liouville operator introduced by Prigogine and others is applied to moderately dense gases interacting through hard-core potentials in arbitrary d-dimensional spaces. Kinetic equations near equilibrium are constructed in each subspace as introduced in the spectral decomposition for collective, renormalized reduced distribution functions. Our renormalization is a nonequilibrium effect, as the renormalization effect disappears at equilibrium. It is remarkable that our renormalized functions strictly obey well-defined Markovian kinetic equations for all d, even though the ordinary distribution functions obey nonMarkovian equations with memory effects. One can now define transport coefficients associated to the collective modes for all dimensional systems including d = 2. Our formulation hence provides a microscopic meaning of the macroscopic transport theory. Moreover, this gives an answer to the long-standing question whether or not transport equations exist in two-dimensional systems. The non-Markovian effects for the ordinary distribution function, such as the long-time tails for arbitrary n-mode coupling, are estimated by superposition of the Markovian evolutions of the dressed distribution functions.