Chaos, Quantization and the Correspondence Principle

巴特曼博士正在研究经典力学和量子力学之间的联系，因为经典系统似乎允许一般的混沌行为，而量子系统则不允许。他提出的一个问题是量子系统混沌的定义。虽然在如何定义经典物理学中的混沌上至少有一些共识，但在量子力学中混沌的定义问题是完全开放的。混沌量子定义的一种方法是采用算法复杂度定义。这种观点的优点在于，它似乎是“理论中立的”。根据这个定义，量子力学完全不适合混沌。巴特曼博士认为，这种定义应该受到抵制，因为它在一定程度上把混沌问题与动力学问题分开了。相反，巴特曼博士认为，对对应原理的正确理解解决了定义量子混沌的问题。对应原理，如果得到正确的解释，已经为经典力学和量子力学提供了一个关于混沌的统一解释。巴特曼博士认为，他所主张的对应原理的解释有历史依据，这可以在尼尔斯·玻尔早期关于量子理论的著作中找到。

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.