Microscopic Approach to Kinetic Theory: Inhomogeneous Systems

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Abstract
The microscopic linearized Vlasov equation is solved in terms of a generalized inverse dielectric function ε−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.