Dynamics in Physical Models

物理模型中的动力学

• 批准号: 0098788
• 负责人: Nikolai Chernov
• 金额: $ 8.45万
• 依托单位: University of Alabama at Birmingham
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-06-01 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0098788&HistoricalAwards=false
• 关键词: Dynamics; Physical; Models

The project is devoted to dynamical systems of physical origin, including Lorentz gases (both in equilibrium and under external forces), hard ball systems, billiards, ideal gases with a massive test particle, and open Hamiltonian systems. Most of these are known (or expected) to have chaotic behavior. Due to recent works of D. Dolgopyat, D. Ruelle, Ya. Sinai, L.-S. Young and others, mathematical tools in the theory of hyperbolic and chaotic dynamical systems appear to be developed far enough to attack many open problems that have been so far only studied heuristically or numerically by physicists, if at all. In particular, we plan to investigate the nature of nonequilibrium steady states by means of Sinai-Ruelle-Bowen measures, time correlation functions that appear in transport laws and diffusion equations, open Hamiltonian systems that admit conditionally invariant measures, the motion of a massive particle in an ideal gas by using an appropriate space-time limit, etc. In each case we aim at obtaining exact results and providing solid rigorous proofs. The general goal of the project is to conduct mathematical studies of facts and phenomena that have attracted attention in physical community and have applications outside of mathematics. In particular, the results would contribute to the mathematical foundation of statistical mechanics and thermodynamics and could strengthen the link between the theory of dynamical systems and physics and other sciences.

该项目致力于物理起源的动力学系统，包括洛伦兹气体（平衡和外力下），硬球系统，台球，具有大质量测试粒子的理想气体和开放的哈密顿系统。其中大多数已知（或预期）具有混沌行为。由于D.多尔戈皮亚特湾Ruelle，Ya.西奈湖S.杨和其他人认为，双曲和混沌动力系统理论中的数学工具似乎已经发展到足以解决许多迄今为止只被物理学家进行了理论或数值研究的开放问题。特别是，我们计划通过Sinai-Ruelle-Bowen措施，出现在输运定律和扩散方程中的时间相关函数，允许条件不变措施的开放Hamilton系统，通过使用适当的时空限制，在每种情况下，我们的目标是获得准确的结果，并提供坚实的严格的证明。该项目的总体目标是对在物理界引起注意并在数学之外有应用的事实和现象进行数学研究。特别是，这些结果将有助于统计力学和热力学的数学基础，并可以加强动力系统理论与物理学和其他科学之间的联系。