Dispersion Interaction Between Thin Conducting Cylinders

The ground state and excited state resonance dipole-dipole interaction energy between two elongated conducting molecules are explored. We review the current status for ground state interactions. This interaction is found to be of a much longer range than in the case when the molecules are pointlike and nonconducting. These are well known results found earlier by Davies, Ninham, and Richmond, and later, using a different formalism, by Rubio and co-workers. We show how the theory can be extended to excited state interactions. A characteristic property following from our calculation is that the interaction energy dependence with separation ($R$) goes like $f(R)/R^2$ both for resonance and for the van der Waals case in the long range limit. In some limits $f(R)$ has a logarithmic dependency and in others it takes constant values. We predict an unusual slow decay rate for the energy transfer between conducting molecules.