  We investigate long-range forces between atoms with anisotropic electric
polarizability interacting with dielectrics having anisotropic permittivity in
the weak-coupling approximation. Unstable configurations in which the force
between the objects is repulsive are constructed. Such configurations exist for
three anisotropic atoms as well as for an anisotropic atom above a dielectric
plate with a hole whose permittivity is anisotropic. Apart from the absolute
magnitude of the force, the dependence on the configuration is qualitatively
the same as for metallic objects for which the anisotropy is a purely geometric
effect. In the weak limit closed analytic expressions for rather complicated
configurations are obtained. The non-monotonic dependence of the interaction
energy on separation is related to the fact that the electromagnetic Green's
dyadic is not positive definite. The analysis in the weak limit is found to
also semi-quantitatively explain the dependence of Casimir forces on the
orientation of anisotropic dielectrics observed experimentally. Contrary to the
scalar case, irreducible electromagnetic three-body energies can change sign.
We trace this to the fact that the electromagnetic Green's dyadic is not
positive definite.
