小粒子在量子真空中会表现出布朗运动吗？
Will small particles exhibit Brownian motion in the quantum vacuum?
摘要：
在有限温度下，小粒子与场相互作用的布朗运动是一种众所周知的现象。在零温度下，即使没有热涨落，量子场仍然具有真空涨落。于是，有趣的问题是，当量子场假定处于真空态时，与量子场相互作用的小粒子是否会表现出布朗运动。本文研究了（1+1）维中小电荷和非理想镜与量子标量场相互作用的情形。将量子场视为经典随机变量，我们写出粒子的朗之万方程。我们表明，我们从这样的方法得到的结果同意从波动耗散定理得到的结果。与有限温度的情况不同，在零温度下不存在特殊的参照系，因此粒子不破坏洛伦兹不变性是必不可少的。我们发现标量荷破坏了洛伦兹不变性，而非完美镜则没有。我们的结论是，小粒子，如不完美的镜子{ \it将}表现出布朗运动，即使在量子真空中，但这种效果可以是如此之小，它可能被证明是很难观察到它的实验。
英文摘要：
The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of a small charge and an imperfect mirror interacting with a quantum scalar field in (1+1) dimensions. Treating the quantum field as a classical stochastic variable, we write down a Langevin equation for the particles. We show that the results we obtain from such an approach agree with the results obtained from the fluctuation-dissipation theorem. Unlike the finite temperature case, there exists no special frame of reference at zero temperature and hence it is essential that the particles do not break Lorentz invariance. We find that that the scalar charge breaks Lorentz invariance, whereas the imperfect mirror does not. We conclude that small particles such as the imperfect mirror {\it will} exhibit Brownian motion even in the quantum vacuum, but this effect can be so small that it may prove to be difficult to observe it experimentally.
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