Numerical and Analytic Studies in Quantum Field Theory and Critical Phenomena

量子场论和临界现象的数值和分析研究

• 批准号: 0099393
• 负责人: Alan Sokal
• 金额: $ 16.99万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0099393&HistoricalAwards=false
• 关键词: Numerical; Analytic; Studies; Quantum; Field

The researchers will develop and apply new and more efficientcomputer algorithms for solving problems in quantum field theory(elementary-particle physics) and the statistical mechanics ofphase transitions and critical phenomena (condensed-matter physics).They will then use these numerical studies to motivate new theoreticalinsights. The research focuses on two principal application areas:lattice spin models and field theories, including lattice gauge theories;and self-avoiding random walk.This work impacts simultaneously on several areas of physical scienceand applied mathematics. Lattice field theories are of direct interestin elementary-particle physics; in particular, lattice gauge theoriesprovide our best model for the strong subnuclear interaction.Lattice spin models are employed to model phase transitionsin numerous areas of condensed-matter physics and physical chemistry.The self-avoiding walk models the behavior of high-molecular-weightpolymer molecules (including proteins and other biopolymers) in solution;it thus has applications in numerous areas of physics, chemistry andchemical engineering, and biophysics.

研究人员将开发和应用新的更有效的计算机算法来解决量子场论（基本粒子物理学）和相变和临界现象的统计力学（凝聚态物理学）中的问题。然后，他们将利用这些数值研究来激发新的理论见解。 研究集中在两个主要的应用领域：晶格自旋模型和场论，包括晶格规范理论;和自避免随机行走。这项工作同时影响物理科学和应用数学的几个领域。 格点场理论在基本粒子物理中有着直接的意义，特别是格点规范理论为强亚核相互作用提供了最好的模型。格点自旋模型在凝聚态物理和物理化学的许多领域中被用来模拟相变。自避免行走模型模拟高分子量聚合物分子的行为（包括蛋白质和其他生物聚合物）在溶液中;因此，它在物理学，化学和化学工程以及生物物理学的许多领域都有应用。