论文标题
量子事件的时间分布
The time distribution of quantum events
论文作者
论文摘要
我们开发了量子事件的时间分布的一般理论，适用于一系列问题，例如到达时间，停留时间和隧道时间。秒表会滴答作响，直到检测到已久的事件为止，此时秒表停止。所期待的事件由投影操作员$π$表示，而理想的秒表被建模为一系列投影测量值，在该测量值中，量子状态用$ \barπ= 1-π$（当期待已久的事件没有发生时）或$π$（当最终发生的事件发生时）。在后续测量之间的$ΔT$的近似值中，我们找到了一个相当简单的通用公式，用于时间分布$ {\ cal p}（t）$，代表了在时间$ t $中检测到已久日事件的概率密度。
We develop a general theory of the time distribution of quantum events, applicable to a large class of problems such as arrival time, dwell time and tunneling time. A stopwatch ticks until an awaited event is detected, at which time the stopwatch stops. The awaited event is represented by a projection operator $π$, while the ideal stopwatch is modeled as a series of projective measurements at which the quantum state gets projected with either $\barπ=1-π$ (when the awaited event does not happen) or $π$ (when the awaited event eventually happens). In the approximation in which the time $δt$ between the subsequent measurements is sufficiently small (but not zero!), we find a fairly simple general formula for the time distribution ${\cal P}(t)$, representing the probability density that the awaited event will be detected at time $t$.
