标题： 一种场论方法用于粗糙度修正 显示英文标题

标题： A Field Theoretic Approach to Roughness Corrections

摘要： 我们开发了一种系统的场论描述，用于平行板的卡西米尔自由能的粗糙度修正。 粗糙度通过指定高度轮廓的相关函数生成泛函来建模，两点相关函数由轮廓的方差\sigma ^2 和相关长度\ell 来表征。 我们得到了一个无质量标量量子场与表面高度轮廓相互作用的配分函数，该相互作用通过一个\delta -函数势。 该模型的配分函数也通过三维耦合标量场在二维平面上的全息约化给出。 带有平行板在分离距离 'a' 的原始三维空间被编码在其边界上的表面场的非局部传播子中。 推导了这个等效的 2+1 维模型的费曼规则，并构建了其抵消项。 该模型的两环贡献给出了自由能的主要粗糙度修正。 到粗糙板的绝对分离距离是测量到一个有效平面的距离，该平面从其轮廓的均值位移了距离\rho \propto \sigma ^2/\ell 。 这种分离的定义消除了自由能中 1/a^4 阶的修正，并导致了一个幺正模型。 我们导出了在极限 \ell \ll a 下的有效低能理论。 它通过单个长度尺度 \rho 来表示非常粗糙板的散射矩阵和有效平面表面。 发现粗糙板上的卡西米尔力随着关联长度 \ell 的减小而始终减弱。 自由能的二环近似在有效低能模型的自由能和接近力近似得到的自由能之间进行插值——对于关联长度为 \sigma \gtrsim 0.5\ell 的非常粗糙板，其作用力在任何分离距离下都比平坦板弱。 显示英文摘要

摘要： We develop a systematic field theoretic description for the roughness correction to the Casimir free energy of parallel plates. Roughness is modeled by specifying a generating functional for correlation functions of the height profile, the two-point correlation function being characterized by the variance, \sigma^2, and correlation length, \ell, of the profile. We obtain the partition function of a massless scalar quantum field interacting with the height profile of the surface via a \delta-function potential. The partition function of this model is also given by a holographic reduction to three coupled scalar fields on a two-dimensional plane. The original three-dimensional space with a parallel plate at separation 'a' is encoded in the non-local propagators of the surface fields on its boundary. Feynman rules for this equivalent 2+1-dimensional model are derived and its counter terms constructed. The two-loop contribution to the free energy of this model gives the leading roughness correction. The absolute separation to a rough plate is measured to an effective plane that is displaced a distance \rho\propto \sigma^2/\ell from the mean of its profile. This definition of the separation eliminates corrections to the free energy of order 1/a^4 and results in a unitary model. We derive an effective low-energy theory in the limit \ell\ll a. It gives the scattering matrix and effective planar surface of a very rough plate in terms of the single length scale \rho. The Casimir force on a rough plate is found to always weaken with decreasing correlation length \ell. The two-loop approximation to the free energy interpolates between the free energy of the effective low-energy model and that obtained in proximity force approximation -- the force on a very rough plate with \sigma\gtrsim 0.5\ell being weaker than on a flat plate at any separation.