Exchange Coulomb interaction in nanotubes: Dispersion of Langmuir waves

Abstract

Microscopic derivation of the Coulomb exchange interaction for electrons located on the nanotubes is presented. Our derivation is based on the many-particle quantum hydrodynamic method. We demonstrate the role of the curvature of the nanocylinders on the force of the exchange interaction. We calculate corresponding dispersion dependencies for electron oscillations on the nanotubes.