Repulsive van der Waals interaction between a quantum particle and a conducting toroid

TL;DR

This paper derives an exact analytical expression for the non-retarded van der Waals force between a quantum particle and a conducting toroid, revealing conditions under which the force becomes repulsive, a rare phenomenon in such systems.

Contribution

It provides the first exact analytical calculation of the dispersion force between a quantum particle and a conducting toroid, highlighting the possibility of repulsive interactions.

Findings

Repulsive van der Waals force can occur with a conducting toroid.

Exact analytical expression for the interaction was obtained.

Repulsion depends on the toroid's radii.

Abstract

We calculate the non-retarded dispersion force exerted on an electrically polarizable quantum particle by a perfectly conducting toroid, which is one of the most common objects exhibiting a non-trivial topology. We employ a convenient method developed by Eberlein and Zietal that essentially relates the quantum problem of calculating dispersion forces between a quantum particle and a perfectly conducting surface of arbitrary shape to a corresponding classical problem of electrostatics. Considering the quantum particle in the symmetry axis of the toroid, we use this method to find an exact analytical result for the van der Waals interaction between the quantum particle and the conducting toroid. Surprisingly, we show that for appropriate values of the two radii of the toroid the dispersive force on the quantum particle is repulsive. This is a remarkable result since repulsion in dispersive interactions involving only electric objects (and particles) in vacuum is rarely reported in the literature. Final comments are made about particular limiting cases as, for instance, the quantum particle-nanoring system.