[Paper Review] On equation of state for the "thermal" part of the spin current: Pauli principle contribution in the spin wave spectrum in cold fermion system

Pavel A. Andreev, L. S. Kuz’menkov|arXiv (Cornell University)|Oct 12, 2015

Dust and Plasma Wave Phenomena5 citations

TL;DR

This paper derives the equation of state for the thermal part of the spin current (TPSC) in degenerate electron and electron-positron plasmas, showing it reduces the frequency of right-circularly polarized spin-plasma waves. The TPSC, arising from Pauli exclusion effects, is incorporated into a generalized non-linear Pauli equation, revealing hybridization between spin-plasma and electromagnetic waves and explaining wave suppression at high TPSC levels.

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.

Motivation & Objective

• To derive an equation of state for the thermal part of the spin current (TPSC) in degenerate quantum plasmas, which had been previously neglected.
• To incorporate the TPSC into the spin current evolution equation and the generalized non-linear Pauli equation, enabling accurate modeling of spin dynamics.
• To analyze the impact of the TPSC on the dispersion relations of spin-plasma waves in electron-ion and electron-positron plasmas.
• To examine the role of the TPSC in modifying quantum vorticity and collective excitations, particularly in the presence of external magnetic fields.
• To demonstrate that the TPSC suppresses right-circularly polarized spin-plasma waves and can lead to wave hybridization with electromagnetic modes.

Proposed method

• Derives the thermal part of the spin current (TPSC) using many-particle quantum hydrodynamics and the Pauli equation, accounting for Pauli exclusion effects.
• Introduces a spinor pressure term in the non-linear Pauli equation that includes the TPSC, enabling self-consistent treatment of spin dynamics.
• Applies the derived TPSC to compute the dispersion relations of transverse waves in electron-ion and electron-positron plasmas under external magnetic fields.
• Solves the modified dispersion equations analytically and numerically, identifying conditions under which spin-plasma waves disappear or hybridize with electromagnetic waves.
• Considers both parallel and perpendicular propagation relative to the external magnetic field, deriving frequency shifts due to TPSC and annihilation interactions.
• Derives the generalized vorticity evolution equation including the TPSC contribution, linking spin dynamics to quantum hydrodynamics.

Experimental results

Research questions

• RQ1 What is the equation of state for the thermal part of the spin current (TPSC) in degenerate quantum plasmas, and how does it arise from Pauli exclusion?
• RQ2 How does the TPSC affect the frequency and stability of spin-plasma waves in electron-ion and electron-positron plasmas?
• RQ3 Under what conditions does the TPSC suppress or hybridize right-circularly polarized spin-plasma waves with electromagnetic waves?
• RQ4 How does the TPSC modify the generalized vorticity evolution in spin-1/2 quantum plasmas?
• RQ5 What role does the TPSC play in the resonance frequency of spin-plasma waves, particularly in the presence of electron-positron annihilation?

Key findings

• The thermal part of the spin current (TPSC) is derived as a Pauli exclusion effect, contributing a pressure-like term in the spin current evolution equation.
• The TPSC reduces the frequency of right-circularly polarized spin-plasma waves propagating both parallel and perpendicular to the external magnetic field.
• For sufficiently large TPSC, the right-circularly polarized spin-plasma wave disappears, indicating a critical threshold for wave propagation.
• When the TPSC and Langmuir frequency are comparable, hybridization occurs between spin-plasma waves and electromagnetic waves, leading to a modified dispersion relation.
• The spin-plasma wave frequency is found to be approximately ω ≈ √(Θ² − Λ²), where Θ includes contributions from magnetic field and TPSC, and Λ arises from electron-positron annihilation.
• The generalized non-linear Pauli equation with the spinor pressure term successfully captures the TPSC effects, enabling analytical solutions for wave dispersion and hybridization.