Dielectric permeability tensor and linear waves in spin-1/2 quantum kinetics with non-trivial equilibrium spin-distribution functions

Abstract

A consideration of waves propagating parallel to the external magnetic field is presented. The dielectric permeability tensor is derived from quantum kinetic equations with non-trivial equilibrium spin-distribution functions in the linear approximation on amplitude of wave perturbations. It is possible to consider equilibrium spin-distribution functions with nonzero z-projection proportional to the difference of the spin distribution function while x-and y-projections are equal to zero. It is called trivial equilibrium spin-distribution functions. In general case, x-and y-projections of the spin-distribution functions are nonzero which is called the non-trivial regime. Corresponding equilibrium solution is found in [Phys. Plasmas 23, 062103 (2016)]. Contribution of the nontrivial part of the spin-distribution function appears in the dielectric permeability tensor in the additive form. It is explicitly found here. Corresponding modification in the dispersion equation for the transverse waves is derived. Contribution of nontrivial part of the spin-distribution function in the spectrum of transverse waves is calculated numerically. It is found that the term caused by the nontrivial part of the spin-distribution function can be comparable with the classic terms for the relatively small wave vectors and frequencies above the cyclotron frequency. In majority of regimes, the extra spin caused term dominates over the spin term found earlier, except the small frequency regime, where their contributions in the whistler spectrum are comparable. A decrease of the lefthand circularly polarized wave frequency, an increase of the high-frequency right-hand circularly polarized wave frequency, and a decrease of frequency changing by an increase of frequency at the growth of the wave vector for the whistler are found. A dramatic decrease of the spin wave frequency resulting in several times larger group velocity of the spin wave is found either. Found dispersion equations are used for obtaining of an effective quantum hydrodynamics reproducing these results. This generalization requires the introduction of corresponding equation of state for the thermal part of the spin current in the spin evolution equation.

Quantum Kinetic Theory of Plasmas

“…we may keep the first non-vanishing terms in a Taylor expansion of the potential in Eq. (24). We then get…”

“…A related phenomena, also dependent on the antisymmetry of the manybody wavefunction of electrons, but considerably more complicated to model mathematically, is the exchange interaction [12][13][14][15][16][17][18], whose importance probably has been undervalued in the recent plasma research literature. Upgrading from the Schrödinger Hamiltonian to the Pauli-Hamiltonian, the spin dynamics enter the picture [19][20][21][22][23][24][25], with physics such as the magnetic dipole force, spin precession, and (spin) magnetization currents. Extending the models to cover the weakly relativistic regime [26][27][28], spin-orbit interaction, Thomas precession and a spin-dependent polarization current are new features of the theory.…”

Quantum kinetic theory of plasmas

“…A related phenomenon, also dependent on the antisymmetry of the many-body wave-function of electrons, but considerably more complicated to model mathematically, is the exchange interaction (Crouseilles et al 2008;Haas 2021;Andreev 2014;Zamanian et al 2013Ekman et al 2015;, whose importance probably has been undervalued in the recent plasma research literature. Upgrading from the Schrödinger Hamiltonian to the Pauli Hamiltonian, the spin dynamics enter the picture (Hurst et al 2014;Brodin et al 2008;Andreev 2016Andreev , 2018Andreev and Kuzmenkov 2017;Andreev 2017), with physics such as the magnetic dipole force, spin precession, and (spin) magnetization currents. Extending the models to cover the weakly relativistic regime (Asenjo et al 2012;Hurst et al 2017;Ekman et al 2021), spin-orbit interaction, Thomas precession, and a spin-dependent polarization current are new features of the theory.…”

Spin-electron-acoustic waves and solitons in high-density degenerate relativistic plasmas

“…[6], [7], [8], [9], [10], [11]. The separate spin evolution kinetic is developed and used as well [12], [13], [14], [15]. Study of the separate spin evolution is part of the field of quantum plasmas developed in the large number of works including [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], where the complete quantum hydrodynamic model derivation based on the trace of the microscopic motion of quantum particles [16], [17], [32], [33], [34].…”