Quanum Phases in Condensed Matter

Yale University, New Haven CT

Investigators

Abstract

This award supports theoretical research in condensed matter physics. An outstanding problem in this field is the simultaneous treatment of strong interactions between electrons and a disordered environment. Recently, the principal investigator and collaborators have found a way to handle these twin problems exactly in quantum dots in the limit of large g, where g is the dot conductance. The trick is to use techniques from random matrix theory that apply to states near the Fermi energy. In the proposed research this opportunity for advancement will be fully explored, fully exploiting numerous exciting possibilities that have just opened up. It is also proposed that these techniques be extended to bulk systems. Quite often our ability to solve a difficult problem is predicated on the identification of a small parameter that tames the difficulties. The proposed small parameter, 1/g, would be the first of its kind to help in the exact solution of the disorder-interaction problem. The principle investigator will continue his work on dissemination of knowledge via public lectures, outreach programs, review articles and textbook writing. The proposed work is expected to further our understanding of quantum dots, which are at the center of nanotechnology, as well as clarify very basic scientific issues in many-body physics. The outreach activities will benefit future generations of physics students at all levels, from elementary school to graduate school. Postdoctoral associates will also be trained. %%% This award supports theoretical research in condensed matter physics. An outstanding problem in this field is the simultaneous treatment of strong interactions between electrons when they are in a disordered environment. The interplay between electrons under these circumstances is at the heart of fundamental condensed matter physics. Combining mathematics developed to describe states in the atomic nucleus with quantum dots, "artificial atoms" at the core of nanotechnology, the principal investigator has developed a way to deal with such electrons in an exact way. This has great potential to advance this core problem in physics and, at the same time, provide new methods to deal with similar problems. The principal investigator is active in writing textbooks, review articles and giving public lectures. ***