Curvature-induced repulsive effect on the lateral Casimir-Polder-van derWaals force

Recently, it was shown that when a single protuberance is introduced on an infinite flat conducting surface, an anisotropic particle, kept constrained to move on a plane above the surface, can feel not only a lateral van der Waals (vdW) force that leads it to the protuberance, but, when the protuberance is narrow enough, a lateral force that moves it away from the protuberance. Although this sign inversion in the lateral vdW force was found to be related to the increasing in the curvature of the protuberance, the role of the curvature was not directly isolated from the effect caused by the remaining infinite planar surface. In this paper, seeking to isolate the sign inversion of the lateral vdW force as a result of the increase in curvature of an object, we consider a perfectly conducting infinite cylinder and investigate the vdW interaction with a neutral polarizable point particle constrained to move in a plane near the cylinder. We show that, under the action of the lateral vdW force, an isotropic polarizable particle is always attracted to the point on the plane which is closest to the cylinder surface. On the other hand, when we have an anisotropic particle, for certain particle orientations, anisotropy, and sufficiently high curvature of the cylinder, this lateral vdW force can manifest a repulsive behavior, moving the particle away from the cylinder. Since, in the literature, the sign inversion in the lateral force was discussed only in the context of the vdW regime, here we also extend this inversion to the Casimir-Polder regime. In addition, we also show that there are classical counterparts of this sign inversion effect, involving a neutral point particle with a permanent electric dipole moment.