In this paper we explicate a method of quantum hydrodynamics (QHD) for the study of the quantum evolution of a system of polarized particles. Though we focused primarily on the two-dimension physical systems, the method is valid for three-dimension and one-dimension systems too. The presented method is based upon the Schrödinger equation. Fundamental QHD equations for charged and neutral particles were derived from the many-particle microscopic Schrödinger equation. The fact that particles possess the electric dipole moment (EDM) was taken into account. The explicated QHD approach was used to study dispersion characteristics of various physical systems. We analyzed dispersion of waves in a twodimension (2D) ion and hole gas placed into an external electric field which is orthogonal to the gas plane. Elementary excitations in a system of neutral polarized particles were studied for 1D, 2D and 3D cases. The polarization dynamics in systems of both neutral and charged particles is shown to cause formation of a new type of waves as well as changes in the dispersion characteristics of already known waves. We also analyzed wave dispersion in 2D exciton systems, in 2D electron-ion plasma and 2D electron-hole plasma. Generation of waves in 3D system neutral particles with EDM by means of the beam of electrons and neutral polarized particles is investigated.

This paper is devoted to studying of dispersion of waves in the magnetized plasma with the spin and exploring of new methods of the generation wave in the plasma. We consider the dispersion of waves, existed in the plasma in consequence of dynamic of the magnetic moments. It is shown there are nine new waves in the magnetized plasma because of the magnetic moments dynamic. We show there are instabilities at propagation of the neutron beam through the plasma. Increments of instabilities caused by neutron beam are calculated. For studying of this effects we generalize and use the method of the many-particle quantum hydrodynamics. Described processes can play important role at calculation of the stability and the safeness of the nuclear reactors and the studying of the processes in the atmosphere of the neutron stars.

Quantum hydrodynamic (QHD) model of charged spin-1/2 particles contains physical quantities defined for all particles of a species including particles with spin-up and with spin-down. Different population of states with different spin direction is included in the spin density (magnetization). In this paper we derive a QHD model, which separately describes spin-up electrons and spin-down electrons. Hence we consider electrons with different projection of spin on the preferable direction as two different species of particles. We show that numbers of particles with different spin direction do not conserve. Hence the continuity equations contain sources of particles. These sources are caused by the interactions of spins with magnetic field. Terms of similar nature arise in the Euler equation. We have that z-projection of the spin density is no longer an independent variable. It is proportional to difference between concentrations of electrons with spin-up and electrons with spindown. In terms of new model we consider propagation of waves in magnetized plasmas of degenerate electrons and motionless ions. We show that new form of QHD equations gives all solutions obtained from traditional form of QHD equations with no distinguish of spin-up and spin-down states. But it also reveals a sound-like solution we call the spin-electron acoustic wave. Coincidence of most solutions is expected since we started derivation with the same basic equation.

Based on a Hamiltonian of a charged particle system with an intrinsic magnetic moment in an external electromagnetic field with the field of magnetic moments, quantum hydrodynamic equations are derived, including the equations for densities of particle number, momentum, magnetic moment, and energy. In the self-consistent field approximation, a closed system of equations is obtained, which provides the basis for investigation of collective physical phenomena in distributed quantum systems. INTRODUCTIONRepresentation of the quantum hydrodynamics for a single particle in the form of hydrodynamic equations was first obtained by Madelung in 1926 [1]. In [2][3][4][5][6][7][8], by analogy with Madelung, the hydrodynamic equations were derived based on the Schrödinger equation for a single particle in an external electromagnetic field. In [9], a hydrodynamic model was constructed from the Schrödinger model nonlinear single-particle equation.For an arbitrary particle number in the system, the space-time evolution of densities of electric charge, current, energy, and polarization of particle spins can be described in a continuous form by the balance equations for particle number, momentum, energy, and magnetic moment. The Coulomb spin-spin interactions were considered in the quantum hydrodynamic equations in [10,11]. Waves in the particle system with an intrinsic magnetic moment were considered in [12,13] based on these equations. In [14], the contribution of the spin-current interaction to the balance equations for the momentum and magnetic moment was considered on the basis of the Breit Hamiltonian without the Thomas half.Bearing in mind the use of mathematical quantum hydrodynamic apparatus to investigate the evolution of physical process characteristics in space and time in problems of scattering and absorption of radiation, neutrons, and charged particles by substance, we derive the quantum hydrodynamic equations, including the energy balance equation, on the basis of the Hamiltonian considering the spin-current interactions together with the Coulomb and spin-spin interactions [10]. According to classical representations, we assume that external sources of electromagnetic field and intrinsic particle magnetic moments contribute to a vector potential value.Based on the balance equations, a closed system of equations is obtained to study the dynamics of collective fields and particle distributions without explicit consideration of the quantum correlation effect. To this end, expressions are found for tensors of kinetic pressure and density of magnetic moment flux through the field characteristics of the particle system entering the equations. This problem, in a definite sense, is analogous to the problem of derivation of the state equations; it is solved below on the basis of the method developed in [15].

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