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

Bright-like soliton solution in quasi-one-dimensional BEC in third order on interaction radius

Nonlinear Schr\"{o}dinger equations and corresponding quantum hydrodynamic (QHD) equations are widely used in studying ultracold boson-fermion mixtures and superconductors. In this article, we show that a more exact account of interaction in Bose-Einstein condensate (BEC), in comparison with the Gross-Pitaevskii (GP) approximation, leads to the existence of a new type of solitons. We use a set of QHD equations in the third order by the interaction radius (TOIR), which corresponds to the GP equation in a first order by the interaction radius. The solution for the soliton in a form of expression for the particle concentration is obtained analytically. The conditions of existence of the soliton are studied. It is shown what solution exists if the interaction between the particles is repulsive. Particle concentration of order of $10^{12}$-$10^{14}$ $cm^{-3}$ has been achieved experimentally for the BEC, the solution exists if the scattering length is of the order of 1 $\mu$m, which can be reached using the Feshbach resonance. It is one of the limit case of existence of new solution. The corresponding scattering length decrease with the increasing of concentration of particles. The investigation of effects in the TOIR approximation gives a more detail information on interaction potentials between the atoms and can be used for a more detail investigation into the potential structure.Comment: 7 pages, 3 figure