Dispersion Interaction Between Thin Conducting Cylinders

TL;DR

This work analyzes dispersion interactions between two thin conducting cylinders, addressing both ground-state van der Waals forces and excited-state resonance interactions in the non-retarded limit. Using a hydrodynamic/plasma model for conducting electrons and a scattering-matrix formalism with Matsubara sums, it derives a dispersion relation and explicit asymptotics for the inter-cylinder energy that scale as $E(R)\sim f(R)/R^2$, with $f(R)$ potentially logarithmic in $R$. The key findings reveal markedly longer-range interactions for conducting cylinders compared to non-conducting or point-like objects, including zero- and finite-temperature behaviors and a slow Förster energy transfer rate. These results have implications for energy transfer and assembly in conducting polymers, DNA-like nanostructures, and nanoscale circuit elements, highlighting strong, non-additive long-range coupling in low-dimensional metallic systems.

Abstract

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.

Figures (1)

• Figure 1: (Colors online) Schematic representation of two conducting elongated molecules in a media where $\varepsilon_1$ and $\varepsilon_2$ dielectric functions of the molecules and $\varepsilon_3$ be dielectric function for the media.