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

TL;DR

This paper investigates how the curvature of a conducting cylinder influences the lateral Casimir-Polder and van der Waals forces, revealing conditions under which these forces become repulsive depending on the surface geometry.

Contribution

It demonstrates the curvature-dependent transition from attractive to repulsive lateral forces in both quantum and classical regimes, highlighting nontrivial geometric effects.

Findings

Repulsive lateral CP force occurs when $x_0/R \u003e 6.44$ for certain orientations.

Similar repulsive behavior in vdW regime for $x_0/R \u003e 2.18$.

Classical counterparts involve particles with permanent electric dipoles.

Abstract

We consider a perfectly conducting infinite cylinder with radius $R$, and investigate the Casimir-Polder (CP) and van der Waals (vdW) interactions with a neutral polarizable particle constrained to move in a plane distant $x_0>R$ from the axis of the cylinder. We show that when the relative curvature $x_0/R \lesssim 6.44$, this particle, under the action of the lateral CP force (which is the projection of the CP force onto the mentioned plane), is attracted to the point on the plane which is closest to the cylinder surface. On the other hand, when $x_0/R \gtrsim 6.44$, we also show that, for certain particle orientations and anisotropy, the lateral CP force can move the particle away from the cylinder. This repulsive behavior of such a component of the CP force reveals a nontrivial dependence of the CP interaction with the surface geometry, specifically of the relative curvature. In the vdW regime, we show that a similar nontrivial repulsive behavior occurs, but for the relative curvature $x_0/R \gtrsim 2.18$, which means that this effect requires a smaller cylinder curvature in the vdW regime than in the CP one. In addition, we also show that there are classical counterparts of these effects, involving a neutral particle with a permanent electric dipole moment. The prediction of such geometric effects on this force may be relevant for a better controlling of the interaction between a particle and a curved surface in classical and quantum physics.