Exact Results in Statistical Mechanics

统计力学的精确结果

• 批准号: 9305930
• 负责人: Sheldon Goldstein
• 金额: $ 5万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-15 至 1995-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9305930&HistoricalAwards=false
• 关键词: Exact; Results; Statistical; Mechanics

9305930 Goldstein The investigator intends to continue his analysis of Bohmian mechanics, which defines a deterministic dynamical system involving a novel combination of ordinary and partial differential equations having remarkable properties. The proposed research involves the analysis of several rather distinct components: 1) the basic mathematical properties of the system itself, such as existence and uniqueness of the dynamics; 2) phenomenology, such as the emergence of the quantum formalism and of the classical limit; and 3) extensions to relativity and covariant gravitation. %%% The importance of the proposed research lies in the following observations. 1) The foundations of quantum theory continue to be mired in confusion and incoherence some sixty five years after its inception. 2) Bohmian mechanics is the natural embedding of Schroedinger's equation -- the mathematical core of almost all interpretations of quantum theory -- into a clear, precise physical theory, emerging if one merely insists that the Schroedinger wave function be relevant to the motion of particles. 3) An appreciation of Bohmian mechanics can be the source of flexibility and clarity when one attempts to apply quantum theory in new directions -- for example, to understand the implications of macroscopic interference effects -- and to new domains, such as quantum gravity. ***

9305930 Goldstein研究者打算继续他对波西米亚力学的分析，波西米亚力学定义了一个确定性动力系统，它涉及具有显著性质的常微分方程和偏微分方程的新组合。所提出的研究涉及对几个相当不同的组成部分的分析：1)系统本身的基本数学性质，如动力学的存在性和唯一性；2)现象学，如量子形式主义和经典极限的出现；(3)对相对论和协变引力的扩展。所提出的研究的重要性在于以下观察结果。1)量子理论的基础在其诞生约65年后仍深陷混乱和不连贯的泥潭。2)波西米亚力学是将薛定谔方程（几乎所有量子理论解释的数学核心）自然嵌入到一个清晰、精确的物理理论中，只要坚持认为薛定谔波函数与粒子的运动有关，它就会出现。3)当一个人试图将量子理论应用于新的方向（例如，理解宏观干涉效应的含义）和新的领域（如量子引力）时，对波西米亚力学的欣赏可以成为灵活性和清晰度的来源。＊＊＊