Novotny, A. Mark
Clay, R. Torsten
Date of Degree
Graduate Thesis - Open Access
Master of Science
College of Arts and Sciences
Department of Physics and Astronomy
A general exact matrix renormalization group method is developed for solving quantum transmission through networks. Using this method transmission of spinless electrons is calculated for a Hanoi network and a (newly introduced) fully connected Bethe lattice. Plots of the transmission and wavefunctions are obtained through application of the derived Renormalization Group recursion relations. The plots reveal band gaps (which has possible application in nano devices) in HN3 networks while no band gaps are observed in HN5 networks. With the fully connected Bethe lattice a drastic reduction in the transmission (in comparison to the normal Bethe lattice) is observed. This reduction can be found to be a purely quantum mechanical effect.
Varghese, Chris, "Quantum Electron Transport through Non-traditional Networks: Transmission Calculations using a Renormalization Group Method" (2010). Theses and Dissertations MSU. 3705.