MICROSCOPIC APPROACH TO KINETIC THEORY - INHOMOGENEOUS SYSTEMS

The microscopic linearized Vlasov equation is solved in terms of a generalized inverse dielectric function ∈-1(r, r′; t, t′) and the initial phase-space density fluctuation. This expression is then used to calculate the density autocorrelation function and to obtain a generalized kinetic equation for plasmas and gravitational gases. It is shown that many of the results for the inhomogeneous system have a close similarity to the corresponding results for homogeneous systems. In particular, the test-particle theory is exhibited and an expression is obtained for the phase-space density of the polarization cloud associated with a test particle.