Chaos, Quantization and the Correspondence Principle

混沌、量子化和对应原理

• 批准号: 9012010
• 负责人: Robert Batterman
• 金额: $ 1.04万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9012010&HistoricalAwards=false
• 关键词: Chaos; Quantization; Correspondence; Principle

Dr. Batterman is investigating the connections between classical and quantum mechanics,in light of the fact that classical systems appear to allow generic chaotic behavior while quantum systems do not. One question he is asking is that of a definition of chaos for quantum systems. While there is at least some consensus on how to define chaos in classical physics,the question of a definition for chaos in quantum mechanics is completely open. One approach to a quantum definition for chaos is to adopt an algorithmic complexity definition. The virtue of this view is that it seems to be "theory neutral." On this definition, quantum mechanics is completely inhospitable to chaos. Dr. Batterman argues that this definition is to be resisted, since to a certain degree it divorces the issue of chaos from the dynamics. Instead, Dr. Batterman argues that a proper understanding of the correspondence principle resolves the problem of defining quantum chaos. The correspondence principle, when properly interpreted already supplies a unified account of chaos--for both classical and quantum mechanics. Dr. Batterman argues that the interpretation of the correspondence principle which he advocates has historical support which can be found in Niels Bohr's early writing on the quantum theory.

巴特曼博士正在调查 经典力学和量子力学， 经典系统似乎允许一般的混沌行为 而量子系统则不然。 他问的一个问题是 量子系统混沌的定义 而 关于如何定义混沌，至少有一些共识。 经典物理学中混沌的定义问题 量子力学是完全开放的。 混沌的量子定义的一种方法是采用 算法复杂性定义。 这种观点的优点是 它似乎是“理论中立”的。“根据这一定义， 量子力学完全不适合混沌。 博士 巴特曼认为，这种定义是要抵制，因为 在某种程度上，它将混乱的问题与 动力学 相反，巴特曼博士认为， 对对应原理的理解解决了 量子混沌的定义 的对应关系 原则，当正确解释已经提供了一个 混沌的统一解释--经典和量子的 力学 巴特曼博士认为， 他所倡导的对应原则具有历史的 可以在尼尔斯·玻尔的早期著作中找到支持， 量子理论