论文标题
量子保镖的确切经典极限
Exact classical limit of the quantum bouncer
论文作者
论文摘要
在本文中，我们开发了一种系统的方法来确定周期性量子系统的经典限制，并将其成功应用于量子弹跳器的问题。众所周知，对于周期系统，经典概率密度不遵循量子概率密度。相反，它遵循大量量子数的限制的局部平均值。在这一事实的指导下，并将经典和量子概率密度作为傅立叶膨胀，在这里我们表明局部平均意味着傅立叶系数在大量子数的极限中相互接近。量子傅立叶系数中的主要术语产生了确切的经典限制，但次要术语也出现，我们可以将其解释为宏观水平上的量子校正。我们将该理论应用于重力场下粒子弹跳的问题，并表明经典概率密度完全从量子分布中恢复。我们表明，对于现实的系统，相对于经典结果，量子校正被强烈抑制（以$ \ sim 10^{-10} $）。
In this paper we develop a systematic approach to determine the classical limit of periodic quantum systems and applied it successfully to the problem of the quantum bouncer. It is well known that, for periodic systems, the classical probability density does not follow the quantum probability density. Instead, it follows the local average in the limit of large quantum numbers. Guided by this fact, and expressing both the classical and quantum probability densities as Fourier expansions, here we show that local averaging implies that the Fourier coefficients approach each other in the limit of large quantum numbers. The leading term in the quantum Fourier coefficient yields the exact classical limit, but subdominant terms also emerge, which we may interpret as quantum corrections at the macroscopic level. We apply this theory to the problem of a particle bouncing under the gravity field and show that the classical probability density is exactly recovered from the quantum distribution. We show that for realistic systems, the quantum corrections are strongly suppressed (by a factor of $\sim 10^{-10}$) with respect to the classical result.
