The Casimir force between two rough surfaces grown through statistical growth models is studied, both theoretically and numerically. The models include the random deposition (RD), the random deposition with surface relaxation (RDSR), and the restricted solid-on-solid growth (RSOS). To calculate the Casimir force, the pairwise summation (PWS) method in [Formula: see text] dimensions is used. First, the force between two growing surfaces with RD equations, Edwards–Wilkinson, (EW) and Kardar–Parisi–Zhang (KPZ) equations is theoretically investigated. Then, using the Monte Carlo simulation, the rough surfaces with RD, RDSR, and RSOS models in [Formula: see text] dimensions are simulated in different growth times, and the Casimir force between each pair of rough surfaces in each time step is calculated. The results show that the force between the surfaces increases as the roughness increases.

中文翻译：

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两个粗糙表面之间的卡西米尔力修正的数值和理论研究

在理论上和数值上研究了通过统计生长模型生长的两个粗糙表面之间的卡西米尔力。这些模型包括随机沉积 (RD)、具有表面松弛的随机沉积 (RDSR) 和受限固对固生长 (RSOS)。为了计算 Casimir 力，使用了 [公式：见文本] 维度中的成对求和 (PWS) 方法。首先，用 RD 方程、Edwards-Wilkinson (EW) 和 Kardar-Parisi-Zhang (KPZ) 方程对两个生长表面之间的力进行了理论上的研究。然后，使用蒙特卡罗模拟，对具有[公式：见正文]维度的RD、RDSR和RSOS模型的粗糙表面在不同的生长时间进行模拟，计算每个时间步长每对粗糙表面之间的卡西米尔力.