In this dissertation, we examine transport phenomena in matter. The approach is two-fold.
We derive, from the Boltzmann equation for multiple scattering, a pair of linked first order equations which can then be manipulated so as to produce a telegrapher's equation. Solutions are given. The method is then applied to a twodimensional model, and again, a telegrapher's equation in two spatial variables is found and solved. In either case, it is noted that the solutions are causal, in contradistinction to diffusion theory, but we also show that,asymptotically, our results reduce to those of diffusion theory.
Attention is then turned to solutions of a one-dimensional Schroedinger equation in which the potential function is described by a finite number of randomly spaced impulses of random height. By solving the Schroedinger equation, it becomes possible to find a transfer matrix whose properties, given suitable conditions, completely determine the eigenvalue spectrum. Computer programs have been written and numerical solutions are given for two types of systems; those having a closed structure and those which are coupled with free space. Each one, when averaged over the ensemble of realizations, yields an expected eigenvalue spectrum for the system whose statistics are known.
Level of Degree
Electrical and Computer Engineering
First Committee Member (Chair)
William Jackson Byatt
Second Committee Member
Third Committee Member
Harold D. Southward
Fourth Committee Member
Richard Jerome Griego
Meirelles, Osorio Chagas. "Electrons In Random Media." (1971). https://digitalrepository.unm.edu/ece_etds/512