Disordered Systems, Supersymmetry, and Quantum Hall Effect

Yale University, New Haven CT

Investigators

Abstract

This award supports theoretical research and education on low-temperature quantum phenomena in condensed matter systems. Areas of focus include the quantum Hall regime of an electron gas, and the more recently developed area of bosonic atoms in traps (not solely Bose condensates), which at high rotation rates are expected to exhibit behavior analogous to the quantum Hall effect. The goal is to understand the ground and excited states, and the properties of the elementary excitations. Another major focus is on disordered systems, in the quantum Hall effect and elsewhere. Here the primary emphasis is on noninteracting fermions in two dimensions, where the phase transitions are ultimately expected to be tractable. This will be addressed by analytical means, using and extending techniques in conformal field theory. New techniques and methods will be introduced whenever this can lead to an advance in physical understanding. While the work will concentrate on deepening the understanding of fundamental properties, connection to experiments will be made wherever possible. Concurrently, the PI is teaching Intensive Introductory Physics to well-prepared incoming undergraduates, which provides opportunities to introduce them to current topics, and writing a book on the Quantum Hall Effect, to further disseminate results of the research. This award also supports graduate student training in condensed matter theory. %%% This award supports theoretical research and education on low-temperature quantum phenomena in condensed matter systems. Areas of focus include the quantum Hall regime of an electron gas practically realized by a two-dimensional electron gas trapped in a semiconductor structure and in a high magnetic field, and the more recently developed area of (bosonic) atoms in atom traps, which at high rotation rates are expected to exhibit behavior analogous to the quantum Hall effect. The goal is to understand the quantum mechanical states of these systems. Another major focus is on the effect of disorder on quantum Hall effect systems and elsewhere. This will be addressed by analytical means, using and extending advanced quantum mechanical techniques. New techniques and methods will be developed whenever this can lead to an advance in physical understanding. While the work will concentrate on deepening the theoretical understanding of fundamental properties, connection to experiments will be made wherever possible. Concurrently, the PI is teaching Intensive Introductory Physics to well-prepared incoming undergraduates, which provides opportunities to introduce them to current topics, and writing a book on the Quantum Hall Effect, to further disseminate results of the research. This award also supports graduate student training in condensed matter theory. ***