In a recent paper, it was shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated surface, a neutral anisotropic polarizable particle in vacuum can be attracted not only to the nearest corrugation peak but also to a valley or an intermediate point between a peak and a valley, with such behaviors called the peak, valley, and intermediate regimes, respectively. In the present paper, we investigate how these regimes are affected by the consideration of two nondispersive semi-infinite dielectrics, ${\epsilon }_1$ and ${\epsilon }_2$, separated by a corrugated interface. Specifically, we study the vdW interaction between a neutral anisotropic polarizable particle, embedded in dielectric ${\epsilon }_2$, and dielectric ${\epsilon }_1$. We show that when ${\epsilon }_2<{\epsilon }_1$, the peak, valley, and intermediate regimes have, apart from numerical factors, behaviors similar to those found for the situation where the particle is in vacuum and interacting with a conducting medium. For the case ${\epsilon }_2>{\epsilon }_1$, one might expect a mere permutation between the peak and valley regimes in comparison to the case ${\epsilon }_2<{\epsilon }_1$. Surprisingly, we find that when ${\epsilon }_2>{\epsilon }_1$, the regimes exhibit a very different and nontrivial behavior. Moreover, we show that similar regimes arise in the classical case involving a neutral polarized particle. The description of how the peak, valley, and intermediate regimes are affected by the presence of dielectrics may be relevant for a better understanding of the interaction between anisotropic particles and corrugated surfaces.

中文翻译：

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存在电介质时横向范德华力的规律

在最近的一篇论文中，表明在完美导电的波纹表面所产生的横向范德华 (vdW) 力的作用下，真空中的中性各向异性可极化粒子不仅可以被吸引到最近的波纹峰，而且到谷或峰与谷之间的中间点，这种行为分别称为峰、谷和中间状态。在本文中，我们研究了这些制度如何受到两种非色散半无限电介质的影响，${\epsilon }_1$ 和 ${\epsilon }_2$，由波纹界面隔开。具体来说，我们研究了嵌入电介质中的中性各向异性可极化粒子之间的 vdW 相互作用。${\epsilon }_2$, 和电介质 ${\epsilon }_1$. 我们证明当${\epsilon }_2<{\epsilon }_1$，除了数值因素外，峰值、谷值和中间状态的行为类似于粒子处于真空中并与导电介质相互作用的情况。对于案例${\epsilon }_2>{\epsilon }_1$, 与情况相比，人们可能会期望峰谷状态之间只是一种排列 ${\epsilon }_2<{\epsilon }_1$. 令人惊讶的是，我们发现当${\epsilon }_2>{\epsilon }_1$，这些政权表现出非常不同且非平凡的行为。此外，我们表明在涉及中性极化粒子的经典情况下会出现类似的情况。峰值、谷值和中间状态如何受电介质的影响的描述可能与更好地理解各向异性粒子和波纹表面之间的相互作用有关。