Inui Norio, Goto Kosuke
Graduate School of Engineering, University of Hyogo, Shosha 2167, Himeji, Hyogo, 671-2201, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052133. doi: 10.1103/PhysRevE.88.052133. Epub 2013 Nov 25.
We study the vertical Brownian motion of a gold particle levitated by a repulsive Casimir force to a silica plate immersed in bromobenzene. The time evolution of the particle distribution starting from an equilibrium position, where the Casimir force and gravitational force are balanced, is considered by solving the Langevin equation using the Monte Carlo method. When the gold particle is very close to the silica plate, the Casimir force changes from repulsive to attractive, and the particle eventually sticks to the surface. The escape rate from a metastable position is calculated by solving the Fokker-Plank equation; it agrees with the value obtained by Kramers' escape theory. The duration of levitation increases as the particle radius increases up to around 2.3 μm. As an example, we show that a 1-μm-diameter gold particle can be levitated for a significantly long time by the repulsive Casimir force at room temperature.
我们研究了一个金粒子在排斥性卡西米尔力作用下悬浮于浸没在溴苯中的二氧化硅平板上方的垂直布朗运动。通过使用蒙特卡罗方法求解朗之万方程，我们考虑了粒子分布从卡西米尔力与重力平衡的平衡位置开始的时间演化。当金粒子非常接近二氧化硅平板时，卡西米尔力从排斥变为吸引，粒子最终会附着在表面。通过求解福克 - 普朗克方程计算了从亚稳态位置的逃逸率；它与通过克莱默斯逃逸理论获得的值一致。悬浮持续时间随着粒子半径增加到约2.3μm而增加。例如，我们表明直径为1μm的金粒子在室温下可通过排斥性卡西米尔力悬浮相当长的时间。
