Dispersion interaction between thin conducting cylinders

The ground state and excited state resonance dipole-dipole interaction energy between two elongated conducting molecules is explored in this study. 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 observed from our calculation is that the interaction energy dependence on separation (R) follows f(R)/R² for both resonance and van der Waals cases in the long-range limit. Under some limits, f(R) has a logarithmic dependency, while under others, it has constant values. We predict an unusual slow decay rate for the energy transfer between conducting molecules.