Equilibrium and Non-Equilibrium Statistical Mechanics

平衡和非平衡统计力学

• 批准号: 0605342
• 负责人: Bruno Nachtergaele
• 金额: $ 14.18万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0605342&HistoricalAwards=false
• 关键词: Equilibrium; Non; Statistical; Mechanics

Equilibrium and Non-equilibrium Statistical MechanicsAbstract of Proposed ResearchBruno Nachtergaele This project will support research on theoretical issues in equilibrium and non-equilibrium quantum statistical mechanics. The main focus is on quantum spin models that arise in condensed matter physics as models for the magnetic properties of a large variety of materials. Apart from the possible applications in material science, the primary goal of the project is to provide new insights in fundamental problems of quantum statistical mechanics and to find rigorous methods for their solution. In particular, I will investigate methods to obtain qualitative and quantitative information about the spectrum of model Hamiltonians such as the Heisenberg model and derive implications of these spectral properties for the dynamics of the system.The main focus is on quantum spin models that arise in condensed matter physics as models for the magnetic properties of a large variety of materials. Due to the close similarity of the mathematics, however, it is expected that the project will also provide useful results for applications in quantum information theory and quantum computation. New directions to be explored include the dynamics of complex quantumsystems and the development of numerical techniques to simulate such systems.

研究摘要bruno Nachtergaele该项目将支持平衡和非平衡量子统计力学的理论问题的研究。主要的焦点是量子自旋模型，出现在凝聚态物理模型为磁性的大量各种材料。除了在材料科学方面的可能应用外，该项目的主要目标是为量子统计力学的基本问题提供新的见解，并找到解决这些问题的严格方法。特别是，我将研究获得模型哈密顿谱（如海森堡模型）的定性和定量信息的方法，并推导这些谱性质对系统动力学的影响。主要的焦点是量子自旋模型，出现在凝聚态物理模型为磁性的大量各种材料。然而，由于数学上的密切相似性，预计该项目也将为量子信息理论和量子计算的应用提供有用的结果。需要探索的新方向包括复杂量子系统的动力学和模拟这些系统的数值技术的发展。