量子力学系统的时间行为
Temporal behavior of quantum mechanical systems
摘要：
综述了量子力学系统的时间行为。我们研究了由二次短时行为引起的所谓量子芝诺效应，以及“生存”振幅的分析性质。结果表明，指数行为是由于存在一个简单的极点在第二黎曼单，而分支点的贡献产生的振幅的幂行为。指数衰减形式在短时间内被抵消，在很长时间内由分支点贡献占主导地位，这给出了前者的高斯行为和后者的幂行为。为了实现量子理论中的指数定律，必须考虑整个系统的某种宏观性质。简要回顾了从量子理论中提取指数衰减律的一些尝试，包括van Hove的开创性工作和他著名的"$λ^2T$"极限。我们澄清这些一般的论点，通过介绍和研究一个可解的动力学模型。量子测量问题的一些影响也进行了讨论，特别是与耗散。
英文摘要：
The temporal behavior of quantum mechanical systems is reviewed. We study the so-called quantum Zeno effect, that arises from the quadratic short-time behavior, and the analytic properties of the ``survival" amplitude. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter. In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system. Some attempts at extracting the exponential decay law from quantum theory, aiming at the master equation, are briefly reviewed, including van Hove's pioneering work and his well-known ``$λ^2T$" limit. We clarify these general arguments by introducing and studying a solvable dynamical model. Some implications for the quantum measurement problem are also discussed, in particular in connection with dissipation.
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