This thesis is the outcome of nearly 18 months of research under Professor Harold Baranger. Our hope is that the disordered model studied here can be successfully applied to a variety of intractable problems in mesoscopic physics. My experience on the project has solidified my opinion that doing innovative and challenging research, and tackling problems whose answers are uncertain to both student and professor, is simply the only way to learn. Thanks to Prof. Baranger and visiting professor Denis Ullmo for their time and support.
ABSTRACT: Mesoscopic systems, such as quantum dots, can be modeled by a combination of electron-electron interactions and single-particle wave function statistics. Using the Anderson Model, we studied various statistics of the two-dimensional disordered quantum system, with special attention to areas that do not agree with random matrix theory, the normal method of approximating quantum chaotic systems. The study of global statistics for the system indicates significant localization effects and wave function correlations even at low disorder. The statistical knowledge is then preliminarily applied to the Coulomb Blockade problem.
Here is the thesis in PDF: Thesis.pdf (about 760 KBytes)