Title page for ETD etd-110498-165301


Type of Document Dissertation
Author Toomire, Bruce Vincent
Author's Email Address bvt@austin.rr.com
URN etd-110498-165301
Title Studies in the Wigner-Poisson and Schroedinger-Poisson Systems
Degree PhD
Department Physics
Advisory Committee
Advisor Name Title
Zweifel, Paul F. Committee Chair
Chang, Lay Nam Committee Member
Ficenec, John R. Committee Member
Hagedorn, George A. Committee Member
Klaus, Martin Committee Member
Slawny, Joseph Committee Member
Keywords
  • Wigner-Poisson Schroedinger-Poisson Quantum Transp
Date of Defense 1998-10-21
Availability unrestricted
Abstract
The need to model the quantum effects in semiconductor devices such as resonance tunneling diodes and quantum dots has lead to an intense study of the Wigner-Poisson (WP) and Schroedinger-Poisson (SP) systems. In this work we present the mathematical analysis of several related models for these systems. These include: a time-dependent model of dissipation in (SP), a quasi-linear (SP) system, a study of the stationary (WP)-(SP) problem with a discussion of the quantum analogue of classical BGK modes and a proof of existence of eigenfunctions for (SP) with periodic boundary conditions, and an examination of the stationary Wigner equations with inflow" boundary conditions. Finally, a proposed numerical scheme for the stationary (SP) system with Boltzmann distribution functions is shown along with its corresponding Bloch equation.
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