This paper presents a new method for the efficient numerical computation of Casimir interactions between objects of arbitrary geometries, composed of materials with arbitrary frequency-dependent electrical properties. Our method formulates the Casimi
r effect as an interaction between effective electric and magnetic current distributions on the surfaces of material bodies, and obtains Casimir energies, forces, and torques from the spectral properties of a matrix that quantifies the interactions of these surface currents. The method can be formulated and understood in two distinct ways: textbf{(1)} as a consequence of 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 in geometries that could not be efficiently handled by any other method, the framework proposed here thus achieves an explicit unification of two seemingly disparate approaches to computational Casimir physics.
We extend a recently introduced method for computing Casimir forces between arbitrarily--shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett._103_ 040401 (2009)] to allow treatment of objects with arbitrary material properties, including i
mperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface--surface separation at which finite--size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters.
We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles non-spheroidal, non-axisymmetric objects
and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally relevant geometries, including crossed cylinders and tetrahedral nanoparticles.
