具有移动边界的空腔场的真空能量密度
Vacuum energy densities of a field in a cavity with a mobile boundary
摘要：
本文研究了具有可动壁的一维和三维腔体内的零点场涨落和相应的场能量密度。移动壁的机械自由度被量子力学地描述，并且它们完全包括在整个系统动力学中。在这个光学机械系统中，场和壁可以通过壁上的辐射压力相互作用，辐射压力由腔内的光子甚至真空波动给出。我们考虑两种情况：一维电磁场和三维标量场，并使用格林函数形式主义，它允许扩展的结果得到的标量场的电磁场。我们表明，腔的移动壁的位置的量子涨落显着影响腔体内的场能量密度，特别是在非常接近的移动壁。从紫外截止频率，相关的腔壁的等离子体频率，这种效果的依赖性进行了讨论。我们还比较了一维电磁场和三维无质量标量场的新结果和最近得到的一维无质量标量场的结果。我们表明，移动壁的存在下，也改变了卡西米尔-波尔德力的极化体放置在腔内，实验检测我们已经考虑的新效果的可能性。
英文摘要：
We consider the zero-point field fluctuations, and the related field energy densities, inside a one-dimensional and a three-dimensional cavity with a mobile wall. The mechanical degrees of freedom of the mobile wall are described quantum mechanically and they are fully included in the overall system dynamics. In this optomechanical system, the field and the wall can interact with each other through the radiation pressure on the wall, given by the photons inside the cavity or even by vacuum fluctuations. We consider two cases: the one-dimensional electromagnetic field and the three-dimensional scalar field, and use the Green's functions formalism, which allows extension of the results obtained for the scalar field to the electromagnetic field. We show that the quantum fluctuations of the position of the cavity's mobile wall significantly affect the field energy density inside the cavity, in particular at the very proximity of the mobile wall. The dependence of this effect from the ultraviolet cutoff frequency, related to the plasma frequency of the cavity walls, is discussed. We also compare our new results for the one-dimensional electromagnetic field and the three-dimensional massless scalar field to results recently obtained for the one-dimensional massless scalar field. We show that the presence of a mobile wall also changes the Casimir-Polder force on a polarizable body placed inside the cavity, giving the possibility to detect experimentally the new effects we have considered.
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