William C. Hall                                                                                        July 3
University of Arkansas at Little Rock
Reup-FOM/SILL



Summer 2002 Student Project Proposal


	I will be working with Professor Lenore Horner, from Southern Illinois 
University at Edwardsville, on a research project related to the fractional 
Quantum Hall effect. Therefore, we have a 2-D electron system. In a 2-D 
system the electrons are confined to a quantum well where motion 
perpendicular to the sample surface is "frozen out," since the excited 
states in that direction require a lot of energy. Specifically, we are 
interested in extended states, which cross the whole system from one 
end of the sample to the other. If the extended states exist, we want to 
know how many there are, what their size is, and how their size varies 
with their energy. These values will depend on the background potential 
(density of the peaks relative to the potential of the magnetic field, shape 
of the peaks, and randomness in the location of these peaks). The highly 
theoretical nature of this project requires that I become familiar with 
various computer programs such as Fortran, so that I may run and 
subsequently analyze various data plots. We need to look at our data 
results, compare them to what other researchers have found, and 
determine what differences, if any, exist between our results and those 
that have been obtained by others previously. We will also investigate 
where the background potential is equivalent to a less that five percent 
filling factor. We feel that our experimental results will have the potential to 
add to the present understanding of how current and heat are conducted 
through various materials. One of the long-term goals of this project is to 
make a significant contribution to the development of a unified theory of 
how extended states behave throughout the range of systems.