Topological Phases, Supersymmetry, and Disordered Systems

拓扑相、超对称性和无序系统

• 批准号: 1005895
• 负责人: Nicholas Read
• 金额: $ 42万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005895&HistoricalAwards=false
• 关键词: Topological; Phases; Supersymmetry; Disordered; Systems

TECHNICAL SUMMARYThe Division of Materials Research and the Division of Mathematical Sciences provide funds for this award. It supports theoretical research and education in the area of low-temperature phenomena in both classical and quantum condensed matter systems. Specifically, these include the quantum Hall regime of an electron gas that occurs in a two-dimensional electron gas in a high magnetic field, with the goal of understanding the non-Abelian topological phases of matter in this and other systems in greater depth. There is now a large experimental and theoretical effort aimed at using such systems for topological quantum computation. Another focus is disordered systems, including non-interacting fermions in two dimensions as in the integer quantum Hall effect, with the use of algebraic techniques applied to lattice models and conformal field theory of critical points. Disordered systems arising from optimization and their connections with statistical physics problems such as classical spin glasses will also be addressed. While the research will concentrate on deepening the understanding of fundamental properties, applications to experiments will be made wherever possible.NONTECHNICAL SUMMARYThe Division of Materials Research and the Division of Mathematical Sciences provide funds for this award. It supports theoretical research and education at the interface of condensed matter physics and mathematics. The ability of electrons sandwiched between semiconductors into thin layers in a high magnetic field to conduct electricity is fixed in discrete amounts. Theory predicts that these remarkable quantum Hall effects signal that electrons in two dimensions in a magnetic field can organize themselves into subtle new states of matter. This award supports research that further explores the nature of these states. Since their prediction, it has been realized that the unusual properties of these new states of matter can form the basis for new kinds of computers, so called topological quantum computers. The operation of these computers would be particularly resistant to noise from the environment that normally spoils essential properties of quantum mechanical states. Learning more about exotic quantum mechanical systems and materials and revealing their technological value requires highly sophisticated mathematics and the creativity behind theoretical physics. The ideas and fundamental knowledge generated by endeavors such as these contribute to future technologies not yet envisioned, but contribute to the foundation of this Nation's future success in global economic competition.

材料研究部和数学科学部为该奖项提供资金。它支持经典和量子凝聚态系统中低温现象领域的理论研究和教育。具体来说，这些包括在高磁场中的二维电子气中发生的电子气的量子霍尔机制，其目标是更深入地理解这个系统和其他系统中物质的非阿贝尔拓扑相。现在有大量的实验和理论努力，旨在使用这样的系统拓扑量子计算。 另一个重点是无序系统，包括在整数量子霍尔效应中的二维非相互作用费米子，使用代数技术应用于晶格模型和临界点的共形场论。无序系统所产生的优化和它们与统计物理问题，如经典自旋玻璃的连接也将得到解决。虽然研究将集中在加深对基本性质的理解，但将尽可能地应用于实验。非技术性总结材料研究部和数学科学部为该奖项提供资金。它支持凝聚态物理和数学界面的理论研究和教育。 在强磁场中，夹在半导体薄层之间的电子导电的能力是固定的。理论预测，这些显著的量子霍尔效应表明，磁场中的二维电子可以将自己组织成微妙的新物质状态。 该奖项支持进一步探索这些国家的性质的研究。自从他们的预测，人们已经意识到，这些新的物质状态的不寻常的属性可以形成新类型的计算机，所谓的拓扑量子计算机的基础。这些计算机的运行将特别抵抗来自环境的噪声，这些噪声通常会破坏量子力学状态的基本特性。更多地了解奇异的量子力学系统和材料，并揭示它们的技术价值，需要高度复杂的数学和理论物理背后的创造力。这些努力所产生的想法和基本知识有助于未来的技术尚未设想，但有助于这个国家在全球经济竞争中未来成功的基础。