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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.

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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We consider quantum plasmas of electrons and motionless ions. We describe separate evolution of spin-up and spin-down electrons. We present corresponding set of quantum hydrodynamic equations. We assume that plasmas are placed in an uniform external magnetic field. We account different occupation of spin-up and spin-down quantum states in equilibrium degenerate plasmas. This effect is included via equations of state for pressure of each species of electrons. We study oblique propagation of longitudinal waves. We show that instead of two well-known waves (the Langmuir wave and the Trivelpiece-Gould wave), plasmas reveal four wave solutions. New solutions exist due to both the separate consideration of spin-up and spin-down electrons and different occupation of spin-up and spin-down quantum states in equilibrium state of degenerate plasmas.