Theory of Quantum Coherence and Measurement Process

薛定谔猫的悖论在量子力学框架内是无法解决的。一个问题是，量子力学是否仍然适用于不仅适用于微观或介观系统，而且适用于真正的宏观系统。考虑到这一根本问题，开展了以下研究：(A)东北大学正在进行的在10mK以下3He-4He过饱和溶液相分离的实验表明，观察到了宏观量子成核(MQN)现象。为了在微观理论的基础上解释这一现象，我们提出了一个能够描述量子成核过程的场论模型。然后，我们继续推导出一个有效的量子力学，它遵循一个相关的集体自由度，即核化气泡的半径R。虽然从这个考虑得到的初步结果基本上给出了与标准唯象模型中设想的控制气泡动力学的势能相同的势能，但它与后者在膨胀气泡的有效惯性质量的R依赖关系上不一致。因此，唯象模型被发现高估了10次方的量子成核速率。(B)在一般情况下，宏观量子现象，例如MQN，会受到测量行为的严重影响。因此，有必要研究由所讨论的宏观系统和相关的测量仪器组成的整个系统。为此，我们提出了一个简单的模型，并得出了以下结论：在某些理想但可实现的情况下，可以进行一种保持量子相干性完好的测量。

The paradox of the Schroedinger's cat will not be resolvable within the framework of quantum mechanics. A question arises whether or not quantum mechanics remains to be applicable not only to a microscopic or mesoscopic system but also to a genuine macroscopic system. With this fundamental problem in mind the following research has been carried out.(a) The experiment under way at Tohoku University on the phase separation of a supersaturated solution of 3He in liquid 4He at temperatures below 10mK suggests that the phenomenon of macroscopic quantum nucleation (MQN) has been observed. With the aim of elucidating this phenomenon on a microscopic-theoretical foundation, we proposed a field-theoretic model which is capable of describing the quantum nucleation process. We then proceeded to deriving an effective quantum mechanics obeyed by a relevant collective degree of freedom, namely radius R of the mucleating bubble. While a preliminary result obtained from this consideration gives essentially the same potential energy governing the dynamics of the bubble as envisaged in the standard phenomenological model, it disagrees with the latter in the R-dependence of the effective inertial mass for the expanding bubble. As a consequence the phenomenological model is found to overestimate the quantum nucleation rate by a factor of 10th power of 10.(b) In general macroscopic quantum phenomena, of which MQN is an example, can be severely affected by the very act of measuring them. It is therefore necessary to investigate the total system consisting of the macrscopic system in question and a relevant measurement apparatus. We proposed a simple model for this purpose and arrived at the following conclusion ; it is possible under certain ideal yet realizable circumstances to conduct a measurement which keeps the quantum coherence under investigation intact.