Studies in the Wigner-Poisson and Schroedinger-Poisson Systems

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Physics

Department dc:contributor.department

Physics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1998

Author dc:creator

• Toomire, Bruce V.

Chair dc:contributor.committeechair

• Zweifel, Paul F.

Committee members dc:contributor.committeemember

• Ficenec, John R.
• Hagedorn, George A.
• Slawny, Joseph
• Klaus, Martin
• Chang, Lay Nam

• Wigner-Poisson Schroedinger-Poisson Quantum Transp

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-110498-165301

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/29464