Universal Scaling Laws for Dispersion Interactions

We study the scaling behavior 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/a7 and 1/a4, respectively, and the Casimir force per unit area by 1/a4. In the short-distance regime, electric and magnetic bodies lead to different scaling behavior. As applications, we present scaling functions for two atom-body potentials and display the equipotential lines of a plate-assisted two-atom potential.