On equations for the evolution of collective phenomena in fermion systems

Abstract

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].

Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas

“…Interaction of magnetic moments with the electric currents is an example of the spin-current interaction, which is not included in this paper, but it can be included by the many-particle quantum hydrodynamic method [3]. The quantum Bohm potential contribution in the magnetic moment balance equation is written in the single particle approximation.…”

“…Classic and quantum hydrodynamics for finite size ions and dust particles was developed in Ref. [66]. We do not need to include finite size of particles in theory of electron-positron plasmas, since modern fundamental theory consider these particles as point-like objects.…”

“…However there are more semi-relativistic effects. They are the spin-current [3] and the current-current [9], [60], [61] interactions, mentioned above, the relativistic correction to kinetic energy (RCKE) [9], [60], [61], and the spin-orbit interaction as well [38], [32]. All these interactions are parts of the Breit Hamiltonian (see [11] section 83).…”

Visible-active photocatalytic behaviors observed in nanostructured lead chalcogenides PbX (X = S, Se, Te)

“…For example, the lattice of these compounds is relative stable over a rather wide range of nonstoichiometry and the temperature coefficients (dEg/dT) are positive while it is negative for all other semiconductors. They have higher carrier mobilities, larger dielectric constants and narrow band gaps which decrease with hydrostatic pressure [14][15][16] and increase with temperature. [15][16][17] These unusual characteristics make them practical in various technological applications, such as infrared opto-electronic devices, thermoelectric devices, photo-voltaic cells, infrared lasers and light-emitting devices.…”

“…They have higher carrier mobilities, larger dielectric constants and narrow band gaps which decrease with hydrostatic pressure [14][15][16] and increase with temperature. [15][16][17] These unusual characteristics make them practical in various technological applications, such as infrared opto-electronic devices, thermoelectric devices, photo-voltaic cells, infrared lasers and light-emitting devices. [18][19][20][21][22][23][24] Narrow band gaps and high carrier mobilities identify lead chalcogenides potential materials for photocatalysis.…”