Universal scaling laws for dispersion interactions

TL;DR

This paper derives universal scaling laws for dispersion interactions, showing how potentials and forces change with geometric rescaling, and provides specific scaling functions and visualizations for atom-body and plate-assisted atom interactions.

Contribution

It establishes general scaling laws for dispersion potentials and forces, including atom-atom, atom-body, and Casimir forces, under geometric rescaling.

Findings

Atom-atom potential scales as 1/a^7 under rescaling.

Atom-body potential scales as 1/a^4 under rescaling.

Casimir force per unit area scales as 1/a^4 under rescaling.

Abstract

We study the scaling behaviour of dispersion potentials and forces under very general conditions. We prove that a rescaling of an arbitrary geometric arrangement by a factor a changes the atom-atom and atom-body potentials in the long-distance limit by factors 1/a^7 and 1/a^4, respectively and the Casimir force per unit area by 1/a^4. In the short-distance regime, electric and magnetic bodies lead to different scaling behaviours. As applications, we present scaling functions for two atom-body potentials and display the equipotential lines of a plate-assisted two-atom potential.