Fluctuating Surface Currents: A New Algorithm for Efficient Prediction of Casimir Interactions among Arbitrary Materials in Arbitrary Geometries. I. Theory

摘要

This paper presents a new method for the efficient numerical computation ofCasimir interactions between objects of arbitrary geometries, composed ofmaterials with arbitrary frequency-dependent electrical properties. Our methodformulates the Casimir effect as an interaction between effective electric andmagnetic current distributions on the surfaces of material bodies, and obtainsCasimir energies, forces, and torques from the spectral properties of a matrixthat quantifies the interactions of these surface currents. The method can beformulated and understood in two distinct ways: \textbf{(1)} as a consequenceof the familiar \textit{stress-tensor} approach to Casimir physics, or,alternatively, \textbf{(2)} as a particular case of the \textit{path-integral}approach to Casimir physics, and we present both formulations in full detail.In addition to providing an algorithm for computing Casimir interactions ingeometries that could not be efficiently handled by any other method, theframework proposed here thus achieves an explicit unification of two seeminglydisparate approaches to computational Casimir physics.