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PublicationStable Levitation and Alignment of Compact Objects by Casimir Spring Forces(2010-02-19) Rahi, Sahand Jamal; Zaheer, SaadWe investigate a stable Casimir force configuration consisting of an object contained inside a spherical or spheroidal cavity filled with a dielectric medium. The spring constant for displacements from the center of the cavity and the dependence of the energy on the relative orientations of the inner object and the cavity walls are computed. We find that the stability of the force equilibrium—unlike the direction of the torque—can be predicted based on the sign of the force between two slabs of the same material. PublicationCasimir interactions of an object inside a spherical metal shell(2010-03-18) Zaheer, Saad; Rahi, Sahand Jamal; Emig, Thorsten; Jaffe, Robert LWe investigate the electromagnetic Casimir interactions of an object contained within an otherwise empty, perfectly conducting spherical shell. For a small object we present analytical calculations of the force, which is directed away from the center of the cavity, and the torque, which tends to align the object opposite to the preferred alignment outside the cavity. For a perfectly conducting sphere as the interior object, we compute the corrections to the proximity force approximation (PFA) numerically. In both cases the results for the interior configuration match smoothly onto those for the corresponding exterior configuration. PublicationCasimir potential of a compact object enclosed by a spherical cavity(2010-11-10) Zaheer, Saad; Rahi, Sahand Jamal; Emig, Thorsten; Jaffe, Robert LWe study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects’ scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the internal object, and the two are sufficiently separated, the Casimir force can be expressed in terms of the static electric and magnetic multipole polarizabilities of the internal object, which is analogous to the Casimir-Polder result. Although it is not a simple power law, the dependence of the force on the separation of the object from the containing sphere is a universal function of its displacement from the center of the sphere, independent of other details of the object’s electromagnetic response. Furthermore, we compute the exact Casimir force between two metallic spheres contained one inside the other at arbitrary separations. Finally, we combine our results with earlier work on the Casimir force between two spheres to obtain data on the leading-order correction to the proximity force approximation for two metallic spheres both outside and within one another.