Test particle motion in a Lorentz gas
Abstract
An expansion of the operator PLe(it(1P)L)LP was used to shape the Zwanzig equation into a generalized FokkerPlanck equation which involves a diffusion tensor depending on the test particle's momentum and the time. The resultant equation was studied in some detail for the case of test particle motion in a weakly coupled Lorentz gas. The diffusion tensor for this system is considered. Some of its properties are calculated; it is computed explicitly for the case of a Gaussian potential of interaction. The equation for the test particle distribution function can be put into the form of an inhomogeneous Schroedinger equation. The term corresponding to the potential energy in the Schroedinger equation is considered. Its structure was studied, and some of its simplest features were used to find the Green's function in the limiting situations of low density and long time.
 Publication:

Ph.D. Thesis
 Pub Date:
 1975
 Bibcode:
 1975PhDT........33G
 Keywords:

 FokkerPlanck Equation;
 Lorentz Gas;
 Particle Motion;
 Distribution Functions;
 Green'S Functions;
 Potential Energy;
 Schroedinger Equation;
 Fluid Mechanics and Heat Transfer