  Similarities between nonlinear electron-plasmon interactions in a cylindrical
mesoscopic system and Kaluza-Klein theories, which stem from the analogy
between the angular coordinate of a nanocylinder with the compactified
coordinates of the Kaluza-Klein theories, have been considered. These
similarities indicate that electron and plasmon states with non-zero angular
momenta exhibit strong long-range interaction with each other via exchange of
plasmons with zero angular momentum. This insight has been confirmed by finding
correspondent solutions of the nonlinear Maxwell equations for interacting
plasmons. Such solutions have important consequences for description of
electromagnetic and transport properties of mesoscopic metallic wires, holes
and rings, such as recent observation of density-dependent spin polarization in
quantum wires. Numerical estimates indicate that the latter effect can be
explained by the electron energy level splitting in the gyration field induced
due to the magneto-optical effect by the current flowing through the quantum
wire.
