Disorder components in surface anchoring orientation of a smectic-A liquid crystalline film (occurring, e.g., due to surface contamination sources) modify the thermal pseudo-Casimir interaction mediated between the bounding surfaces of the film. By considering a plane-parallel slab with bounding surfaces positioned normal to the layering field of the film, we study the anchoring disorder effects by assuming that the disorder source is present on one of the two substrates, producing a Gaussian-weighted distribution for the preferred molecular anchoring orientation (easy axis) on that substrate, with a finite mean and variance or, more generally, with a homogeneous in-plane, twopoint correlation function. We show that the presence of disorder, either of quenched or annealed type, leads to a significant reduction in the magnitude of the net pseudo-Casimir force between the confining substrates of the film. This force can be attractive or repulsive depending on the boundary conditions. In the quenched case, the interaction force reduction is a direct consequence of an additive free energy term dependent on the variance of the disorder, while in the annealed case, the suppression of the interaction force can be understood based on a disorder-renormalized, effective anchoring strength. We predict a regime of behavior, exhibiting non-monotonic dependence for the interaction pressure as a function of separation. We also show that, by increasing the disorder variance, the interaction pressure changes sign and becomes a monotonically decreasing function of the separation between the substrates.

中文翻译：

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近晶-A液晶薄膜中的表面排列紊乱和热卡西米尔力

近晶-A液晶膜的表面锚定取向中的无序成分（发生，例如，由于表面污染源）改变了膜的边界表面之间介导的热伪卡西米尔相互作用。通过考虑边界面垂直于薄膜分层场的平面平行板，我们通过假设无序源存在于两个基板之一上来研究锚定无序效应，从而为优选的衬底产生高斯加权分布分子锚定方向（易轴），具有有限的均值和方差，或更一般地说，具有均匀的平面内两点相关函数。我们表明，无论是淬火还是退火类型的无序的存在，导致膜的限制基板之间的净伪卡西米尔力的大小显着降低。根据边界条件，该力可以是有吸引力的或排斥的。在淬火的情况下，相互作用力的减少是依赖于无序方差的加性自由能项的直接结果，而在退火的情况下，相互作用力的抑制可以基于无序重整化，有效锚固强度。我们预测了一种行为，表现出对作为分离函数的相互作用压力的非单调依赖性。我们还表明，通过增加无序方差，相互作用压力会改变符号并成为基材之间分离的单调递减函数。