Eigenvalue Statistics for Random Block Operators
| dc.contributor.author | Schmidt, Daniel F. | en |
| dc.contributor.committeechair | Elgart, Alexander | en |
| dc.contributor.committeemember | Hagedorn, George A. | en |
| dc.contributor.committeemember | Klaus, Martin | en |
| dc.contributor.committeemember | Ball, Joseph A. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2015-04-29T08:02:11Z | en |
| dc.date.available | 2015-04-29T08:02:11Z | en |
| dc.date.issued | 2015-04-28 | en |
| dc.description.abstract | The Schrodinger Hamiltonian for a single electron in a crystalline solid with independent, identically distributed (i.i.d.) single-site potentials has been well studied. It has the form of a diagonal potential energy operator, which contains the random variables, plus a kinetic energy operator, which is deterministic. In the less-understood cases of multiple interacting charge carriers, or of correlated random variables, the Hamiltonian can take the form of a random block-diagonal operator, plus the usual kinetic energy term. Thus, it is of interest to understand the eigenvalue statistics for such operators. In this work, we establish a criterion under which certain random block operators will be guaranteed to satisfy Wegner, Minami, and higher-order estimates. This criterion is phrased in terms of properties of individual blocks of the Hamiltonian. We will then verify the input conditions of this criterion for a certain quasiparticle model with i.i.d. single-site potentials. Next, we will present a progress report on a project to verify the same input conditions for a class of one-dimensional, single-particle alloy-type models. These two results should be sufficient to demonstrate the utility of the criterion as a method of proving Wegner and Minami estimates for random block operators. | en |
| dc.description.degree | Ph. D. | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:4806 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/51851 | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | Eigenvalue statistics | en |
| dc.subject | Wegner estimate | en |
| dc.subject | Minami estimate | en |
| dc.subject | Schrodinger operator | en |
| dc.title | Eigenvalue Statistics for Random Block Operators | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |