弱值的时间导数
Time Derivatives of Weak Values
AI总结：
本文研究了弱值的时间导数，揭示了其在量子力学中的物理意义，并提出了确保弱值规范不变性的条件。
摘要：
物理性质的时间导数往往会产生另一个有意义的性质。由于弱值提供了无法从期望值中推导出的实证见解，本文探讨了从弱值的时间导数中可以获得哪些物理性质。它证明，一般来说，规范不变的弱值的时间导数既不是弱值也不是规范不变的量。提出了两个条件，以确保弱值的左或右时间导数也是规范不变的弱值。在这些条件下，可以为弱值推导出一个局部的埃亨费斯特类定理，为弱值的时间导数提供了自然的解释。值得注意的是，一个系统的位移的弱值测量提供了关于两个额外未测量的弱值的信息：系统的局部速度和加速度，分别通过初始弱值的一阶和二阶时间导数获得。这些发现还为实验者提供了将弱值理论转化为实际实验室设置的指导，为创新的量子技术铺平了道路。一个例子说明了如何通过弱值位置的一阶和二阶时间导数确定电磁场在特定位置和时间的值。
英文摘要：
The time derivative of a physical property often gives rise to another meaningful property. Since weak values provide empirical insights that cannot be derived from expectation values, this paper explores what physical properties can be obtained from the time derivative of weak values. It demonstrates that, in general, the time derivative of a gauge-invariant weak value is neither a weak value nor a gauge-invariant quantity. Two conditions are presented to ensure that the left- or right-time derivative of a weak value is also a gauge-invariant weak value. Under these conditions, a local Ehrenfest-like theorem can be derived for weak values giving a natural interpretation for the time derivative of weak values. Notably, a single measured weak value of the system's position provides information about two additional unmeasured weak values: the system's local velocity and acceleration, through the first- and second-order time derivatives of the initial weak value, respectively. These findings also offer guidelines for experimentalists to translate the weak value theory into practical laboratory setups, paving the way for innovative quantum technologies. An example illustrates how the electromagnetic field can be determined at specific positions and times from the first- and second-order time derivatives of a weak value of position.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
