4 research outputs found
Test particle motion in a Lorentz gas
This is a two-part thesis concerning the motion of a test
particle in a bath. In part one we use an expansion of the operator
PLeit(1-P)LLP to shape the Zwanzig equation into a generalized
Fokker-Planck equation which involves a diffusion tensor depending
on the test particle's momentum and the time.
In part two the resultant equation is 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 is studied, and some of its
simplest features are used to find the Green's function in the
limiting situations of low density and long time.</p