论文标题
牛顿的方程式来自真空中宏观机构的量子力学
Newton's equations from quantum mechanics for a macroscopic body in the vacuum
论文作者
论文摘要
牛顿力量定律$ \ frac {d {\ bf p}} {dt} = {\ bf f} $是源自schrödinger方程的孤立宏观体，例如$ n \ sim 10^{25}，10^{51} {51}的复合状态，$ n \ sim sim $ nite $ and and and and and and and an。在这种情况下，我们首先回顾了量子力学（QM）的三个方面：（i）海森伯格的质量中心（cm）的不确定性关系，（ii）C.M.的扩散。波数据包和（iii）有限的身体温度，暗示着体内的（混合）身体：光子的排放和自定义。他们解释了宏观身体的经典轨迹的起源。 $ r_q $与其CM的量子波动相比的范围$ r_q $有效的比率，并且人体（线性）尺寸$ L_0 $，$ R_Q / L_Q / L_0 \ LINSESIM 1 $或$ R_Q / L_Q / L_0 \ GG 1 $，告诉人体的CM是经典的或量子上的CM，分别是机械上的。在第一种情况下，牛顿的部队法律的CM是ehrenfest定理的。我们为弱重力，谐波振荡电势以及恒定的外部电磁场在空间中缓慢变化而说明了这一点。还讨论了多体系统的规范汉密尔顿方程的推导。由于人体的有限大小（例如重力潮汐力）引起的影响出现在扰动理论中。我们的工作与众所周知的想法一致，即QM中古典物理的出现是由于环境引起的破坏，但是通过阐明牛顿方程式从QM遵循的条件并明确地得出的条件，从而对其进行补充并完成。
Newton's force law $\frac{d {\bf P}}{dt} = {\bf F}$ is derived from the Schrödinger equation for isolated macroscopic bodies, composite states of e.g., $N\sim 10^{25}, 10^{51}, \ldots$ atoms and molecules, at finite body temperatures. We first review three aspects of quantum mechanics (QM) in this context: (i) Heisenberg's uncertainty relations for their center of mass (CM), (ii) the diffusion of the C.M. wave packet, and (iii) a finite body-temperature which implies a metastable (mixed-) state of the body: photon emissions and self-decoherence. They explain the origin of the classical trajectory for a macroscopic body. The ratio between the range $R_q$ over which the quantum fluctuations of its CM are effective, and the body's (linear) size $L_0$, $R_q /L_0 \lesssim 1$ or $R_q/ L_0 \gg 1$, tells whether the body's CM behaves classically or quantum mechanically, respectively. In the first case, Newton's force law for its CM follows from the Ehrenfest theorem. We illustrate this for weak gravitational forces, a harmonic-oscillator potential, and for constant external electromagnetic fields slowly varying in space. The derivation of the canonical Hamilton equations for many-body systems is also discussed. Effects due to the body's finite size such as the gravitational tidal forces appear in perturbation theory. Our work is consistent with the well-known idea that the emergence of classical physics in QM is due to the environment-induced decoherence, but complements and completes it, by clarifying the conditions under which Newton's equations follow from QM, and by deriving them explicitly.
