On the equation of state for the “thermal” part of the spin current: The Pauli principle contribution in the spin wave spectrum in a cold fermion system

Abstract

Spin evolution opened a large field in quantum plasma research. The spin waves in plasmas were considered among new phenomena considered in spin-1/2 quantum plasmas. The spin density evolution equation found by means of the many-particle quantum hydrodynamics shows existence of the "thermal" part of the spin current, which is an analog of the thermal pressure, or the Fermi pressure for degenerate electron gas, existing in the Euler equation. However, this term has been dropped, since there has not been found any equation of state for the thermal part of the spin current (TPSC), like we have for the pressure. In this paper we derive the equation of state for the TPSC and apply it for study of spectrum of collective excitations in spin-1/2 quantum plasmas. We focus our research on the spectrum of spin waves, since this spectrum is affected by the thermal part of the spin current. We consider two kinds of plasmas: electron-ion plasma with motionless ions and degenerate electrons, and degenerate electron-positron plasmas. We also present the non-linear Pauli equation with the spinor pressure term containing described effects. The thermal part of the flux of spin current existing in the spin current evolution equation is also derived. We also consider the contribution of the TPSC in the grand generalized vorticity evolution.

Separated spin evolution quantum hydrodynamics of degenerate electrons with spin–orbit interaction and extraordinary wave spectrum

“…Vector in the spin evolution equations (5.6) is the divergence of the thermal part of the spin current tensor . In accordance with the NLPE equation, as it was demonstrated in Andreev & Kuz’menkov (2015 c ), we have Due to its nature we can also call this the Fermi spin current.…”

“…We use the nonlinear Pauli equation (NLPE) derived in Andreev & Kuz’menkov (2012) for spin- quantum plasmas with spin–orbit interaction. Following Andreev & Kuz’menkov (2015 c ) we generalize the NLPE to include the spinor pressure. We apply the generalized NLPE to derive the SSE-QHD with the spin–orbit interaction and the Fermi spin current.…”

“…The SSE affects the ordinary electromagnetic wave and spin-plasma wave having an electric field oscillating in the direction of the external magnetic field B ext = B 0 e z via the Fermi spin current. This effect is described in Andreev & Kuz'menkov (2015c). Therefore, we do not discuss the ordinary electromagnetic wave and spin-plasma wave in this paper.…”

“…It is demonstrated that the separate spin evolution quantum hydrodynamics (SSE-QHD) leads to existence of the spin-electron acoustic waves (SEAWs) (Andreev 2015 b ; Andreev & Kuz’menkov 2015 b ; Andreev & Iqbal 2016) and allows us to derive an equation of state for the thermal part of the spin current in the regime of degenerate electrons (Andreev & Kuz’menkov 2015 c ), where the distribution of electrons in the quantum states is caused by Pauli blocking.…”

“…The SSE-QHD is generalized to consider the spin current evolution (Trukhanova 2015). An equation of state for the spin current flux (Andreev & Kuz’menkov 2015 a ; Trukhanova 2015) is also derived via SSE-QHD (Andreev & Kuz’menkov 2015 c ). The Coulomb exchange interaction is included in SSE-QHD in Andreev (2016 a ).…”