Separated spin-up and spin-down evolution of degenerated electrons in two dimensional systems: Dispersion of longitudinal collective excitations in plane and nanotube geometry

Applying the separated spin evolution quantum hydrodynamics to two-dimensional electron gas in plane samples and nanotubes located in external magnetic fields we find new kind of wave in electron gas, which is called the spin-electron acoustic wave. Separate spin-up electrons and spin-down electrons evolution reveals in replacement of the Langmuir wave by the couple of hybrid waves. One of two hybrid waves is the modified Langmuir wave. Another hybrid wave is the spin-electron acoustic wave. We study dispersion of these waves in two dimensional structures of electrons. We also consider dependence of dispersion properties on spin polarisation of electrons in external magnetic field.Comment: 5 pages, 5 figure