Casimir-Polder energy landscape: Unipolarizable atom and ring
The paper derives an exact mathematical expression for the Casimir-Polder interaction energy between a point atom and a dielectric ring using complete elliptic integrals. This generalization allows researchers to analyze atomic stability not just on the ring's axis, but at any position off-axis. The resulting energy landscape analysis reveals that equilibrium points can be unstable, suggesting potential violations of the Earnshaw theorem in vacuum fluctuation systems.