标题： 量子经典到达时间分布的概率流比较 显示英文标题

标题： The Quantum-Classical Comparison of the Arrival Time Distribution through the Probability Current

摘要： 我们考虑通过量子概率流定义的到达时间分布，以研究量子力学中自由粒子的高斯波包的到达时间的经典极限问题。 我们为由相空间分布函数表示的自由粒子系综构造了到达时间分布的经典对应量，该分布函数在经典刘维尔方程下演化。 这样构建的经典概率流在最小不确定性极限下与量子概率流相匹配。 此外，可以一般性地证明，在粒子质量较大的极限下，可以从量子力学的概率流和平均到达时间平滑地过渡到它们相应的经典值。 显示英文摘要

摘要： We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We formulate the classical analogue of the arrival time distribution for an ensemble of free particles represented by a phase space distribution function evolving under the classical Liouville's equation. The classical probability current so constructed matches with the quantum probability current in the limit of minimum uncertainty. Further, it is possible to show in general that smooth transitions from the quantum mechanical probability current and the mean arrival time to their respective classical values are obtained in the limit of large mass of the particles.