CAREER: Geometry and Interference in Strongly Correlated Systems

职业：强相关系统中的几何和干涉

• 批准号: 0348358
• 负责人: Alexander Abanov
• 金额: --
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2010-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0348358&HistoricalAwards=false
• 关键词: CAREER; Geometry; Interference; Strongly; Correlated

This CAREER award is co-funded by the Materials Theory program of the Division of Materials Research and the Topology program of the Division of Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. This CAREER award supports theoretical research and education involving the application of topological methods and new theoretical methods to outstanding problems in condensed matter theory. The research will establish a basis for further studies of the physics of strongly correlated and disordered systems. Research thrusts include: (i) calculating the probability of phase slips in superconducting wires with applications to existing experiments, (ii) developing an effective low energy description in the presence of singular configurations, (iii) applying topological analysis and instanton calculus to the Coulomb blockade problem, (iv) developing a hydrodynamic approach as a non-linear bosonization to calculate the asymptotic behavior of correlation functions. In contrast to the symmetry analysis broadly used in condensed matter theory, topological analysis has not yet been widely accepted by the condensed matter community. This type of analysis has the potential to solve or to help solve many open problems. The proposed research will promote the use of topological methods in condensed matter theory and will strengthen connections with quantum field theory and mathematical physics. Some of the problems considered are deeply rooted in modern mathematics. Pursuing topological studies in condensed matter should turn out mutually beneficial for both condensed matter theory and mathematical physics.The educational component involves several activities that will be integrated with the research: (i) A review and lectures on topological methods in condensed matter physics will fill an important gap in graduate student (and more generally, condensed matter physics) education. These methods play an increasingly important role in modern physics. Creation of a new course on the use of topological methods with supporting materials on the Internet will reach a broader segment of the physics community and students. (ii) A new graduate course on Quantum magnetism will be developed to enhance graduate education and to bring together students from different research groups. (iii) Student symposia will be organized which, together with a strategy for attracting visitors to stay for longer times, will enhance education of graduate and undergraduate students from different research groups and will facilitate their active participation in research at earlier stages of their careers. (iv) A 'minimal set' of problems will be created for every mandatory graduate course to establish a common core for the physics department. It will be available online and may provide a resource for students and teaching faculty outside of the department.%%%This CAREER award is co-funded by the Materials Theory program of the Division of Materials Research and the Topology program of the Division of Mathematical Sciences under the umbrella of the NSF-wide Mathematical Sciences Priority Area. This CAREER award supports theoretical research and education involving the application of advanced mathematical methods based on geometry and topology to outstanding problems in condensed matter theory. The PI will combine these methods with other advanced theoretical techniques and focus on a set of problems that seem ripe for advance from this viewpoint. Work on these problems will lay a foundation to attack the notoriously difficult and important problem of the nature of electronic states that arise from strong electron-electron interactions and disorder.In contrast to the symmetry analysis broadly used in condensed matter theory, topological analysis has not yet been widely accepted by the condensed matter community. This type of analysis has the potential to solve or to help solve many open problems. The proposed research will promote the use of topological methods in condensed matter theory and will strengthen the connections with quantum field theory and mathematical physics. Some of the problems considered are deeply rooted in modern mathematics. Pursuing topological studies in condensed matter should turn out mutually beneficial for both condensed matter theory and mathematical physics.The educational component involves several activities that will be integrated with the research: (i) A review and lectures on topological methods in condensed matter physics will fill an important gap in graduate student (and more generally, condensed matter physics) education. These methods play an increasingly important role in modern physics. Creation of a new course on the use of topological methods with supporting materials on the Internet will reach a broader segment of the physics community and students. (ii) A new graduate course on Quantum magnetism will be developed to enhance graduate education and to bring together students from different research groups. (iii) Student symposia will be organized which, together with a strategy for attracting visitors to stay for longer times, will enhance education of graduate and undergraduate students from different research groups and will facilitate their active participation in research at earlier stages of their careers. (iv) A 'minimal set' of problems will be created for every mandatory graduate course to establish a common core for the physics department. It will be available online and may provide a resource for students and teaching faculty outside of the department.***

该职业奖由材料研究部的材料理论计划和数学科学部的拓扑计划共同资助，该计划隶属于NSF范围内的数学科学优先领域。 该职业奖支持理论研究和教育，涉及拓扑方法和新的理论方法在凝聚态理论中的突出问题的应用。该研究为进一步研究强关联和无序系统的物理奠定了基础。研究重点包括：（i）计算超导导线中相位滑移的概率，并将其应用于现有的实验;（ii）在奇异组态的存在下发展一种有效的低能描述;（iii）将拓扑分析和瞬子演算应用于库仑阻塞问题;（iv）发展一种作为非线性玻色化的流体动力学方法来计算相关函数的渐近行为。与凝聚态理论中广泛使用的对称性分析相反，拓扑分析尚未被凝聚态理论界广泛接受。这种类型的分析有可能解决或帮助解决许多悬而未决的问题。拟议的研究将促进拓扑方法在凝聚态理论中的使用，并将加强与量子场论和数学物理的联系。有些问题被认为是深深植根于现代数学。在凝聚态物理学中进行拓扑学的研究应该对凝聚态理论和数学物理学都是有益的。教育部分包括将与研究相结合的几项活动：（i）关于凝聚态物理学中拓扑学方法的回顾和讲座将填补研究生（更广泛地说，凝聚态物理学）教育的一个重要空白。这些方法在现代物理学中起着越来越重要的作用。开设一门关于使用拓扑方法的新课程，并在因特网上提供辅助材料，这将使物理学界和学生的范围更广。(ii)一个新的量子磁学研究生课程将开发，以加强研究生教育，并汇集来自不同研究小组的学生。(iii)将组织学生座谈会，连同吸引游客逗留更长时间的战略，将加强来自不同研究小组的研究生和本科生的教育，并将促进他们在职业生涯的早期阶段积极参与研究。(iv)一个“最小集”的问题将被创建为每一个强制性的研究生课程，以建立一个共同的核心物理系。它将在线提供，并可能为系外的学生和教师提供资源。%该职业奖由材料研究部的材料理论计划和数学科学部的拓扑计划共同资助，该计划隶属于NSF范围内的数学科学优先领域。 该职业奖支持理论研究和教育，涉及基于几何和拓扑学的高级数学方法在凝聚态理论中的突出问题的应用。PI将联合收割机将这些方法与其他先进的理论技术相结合，并专注于一系列从这个观点来看似乎已经成熟的问题。对这些问题的研究将为解决电子态的本质问题奠定基础。电子态的本质问题是由强电子-电子相互作用和无序引起的。与凝聚态理论中广泛使用的对称性分析相比，拓扑分析尚未被凝聚态学界广泛接受。这种类型的分析有可能解决或帮助解决许多悬而未决的问题。拟议的研究将促进拓扑方法在凝聚态理论中的使用，并将加强与量子场论和数学物理的联系。有些问题被认为是深深植根于现代数学。在凝聚态物理学中进行拓扑学的研究应该对凝聚态理论和数学物理学都是有益的。教育部分包括将与研究相结合的几项活动：（i）关于凝聚态物理学中拓扑学方法的回顾和讲座将填补研究生（更广泛地说，凝聚态物理学）教育的一个重要空白。这些方法在现代物理学中起着越来越重要的作用。开设一门关于使用拓扑方法的新课程，并在因特网上提供辅助材料，这将使物理学界和学生的范围更广。(ii)一个新的量子磁学研究生课程将开发，以加强研究生教育，并汇集来自不同研究小组的学生。(iii)将组织学生座谈会，并制定吸引游客长期逗留的战略，以加强对来自不同研究小组的研究生和本科生的教育，并促进他们在职业生涯的早期阶段积极参与研究。(iv)一个“最小集”的问题将被创建为每一个强制性的研究生课程，以建立一个共同的核心物理系。它将在网上提供，并可能为学生和系外的教师提供资源。