Disordered Systems, Supersymmetry, and Quantum Hall Effect

该奖项支持凝聚态系统中低温量子现象的理论研究和教育。重点领域包括电子气的量子霍尔机制，以及最近开发的陷阱中玻色子原子的区域（不仅仅是玻色凝聚体），预计在高旋转速率下会表现出类似于量子霍尔效应的行为。目标是了解基态和激发态，以及基元激发的性质。另一个主要的焦点是无序系统，在量子霍尔效应和其他地方。这里的主要重点是在二维非相互作用的费米子，其中的相变最终预计是易处理的。这将解决的分析手段，使用和扩展技术共形场理论。新的技术和方法将被引入，只要这可以导致物理理解的进步。虽然工作将集中在加深对基本性质的理解，但将尽可能与实验联系起来。与此同时，PI正在向准备充分的即将入学的本科生教授密集的入门物理学，这为他们提供了向他们介绍当前主题的机会，并撰写了一本关于量子霍尔效应的书，以进一步传播研究成果。该奖项还支持凝聚态理论的研究生培训。%该奖项支持凝聚态系统中低温量子现象的理论研究和教育。重点领域包括电子气的量子霍尔机制，实际上是由半导体结构和高磁场中捕获的二维电子气实现的，以及最近开发的原子陷阱中的（玻色子）原子区域，在高旋转速率下，预计将表现出类似于量子霍尔效应的行为。我们的目标是了解这些系统的量子力学状态。另一个主要的焦点是无序对量子霍尔效应系统和其他地方的影响。这将通过分析手段，使用和扩展先进的量子力学技术来解决。新的技术和方法将被开发，只要这可以导致物理理解的进步。虽然工作将集中在深化基本属性的理论理解，连接到实验将尽可能。与此同时，PI正在向准备充分的即将入学的本科生教授密集的入门物理学，这为他们提供了向他们介绍当前主题的机会，并撰写了一本关于量子霍尔效应的书，以进一步传播研究成果。该奖项还支持凝聚态理论的研究生培训。

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.***