Exchange Coulomb interaction in nanotubes: Dispersion of Langmuir waves

The microscopic derivation of the Coulomb exchange interaction for electrons located on the nanotubes is presented. The derivation is based on the many-particle quantum hydrodynamic method. We demonstrate the effect of curvature of the nanocylinders on the force of exchange interaction. We calculate corresponding dispersion dependencies for electron oscillations on the nanotubes. (C) 2015 AIP Publishing LLC.