Virtual photons in imaginary time: Computing exact Casimir forces using standard computational electromagnetism

Alejandro Rodriguez, Massachusetts Institute of Technology


One of the most dramatic manifestations of quantum electrodynamics observed in the last half-century is the Casimir force: a tiny force on an uncharged, source-free body due to changes in the zero-point energy associated with quantum vacuum fluctuations (virtual photons). We describe a numerical method to compute Casimir forces between arbitrary objects and materials, and to any desired accuracy. Our method, based on integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green’s function for imaginary frequencies, or equivalently, for imaginary time. In particular, we show that a piston-like geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising non-monotonic “lateral” force arising from the walls.

Abstract Author(s): Alejandro Rodriguez, Mihai Ibannescu, Davide Iannuzzi, Federico Capasso, John D. Joannopoulos and Steven G. Johnson.