A general quantum dispersion equation for electron-positron(hole)-ion quantum plasmas is derived and studied for some interesting cases. In an electron-positron degenerate Fermi gas, with or without the Madelung term, a new type of zero sound waves are found. Whereas in an electron-hole plasmas a new longitudinal quantum waves are revealed, which have no analogies in quantum electron-ion plasmas. The excitation of these quantum waves by a low-density monoenergetic straight electron beam is examined. Furthermore, the KdV equation for novel quantum waves is derived and the contribution of the Madelung term in the formation of the KdV solitons is discussed.
We have derived the electrostatic dispersion relation in a magnetized plasma using a recently developed quantum kinetic model based on the Dirac equation. The model contains weakly relativistic spin effects such as Thomas precession, the polarization currents associated with the spin and the spin-orbit coupling. It turns out that for strictly electrostatic perturbations the non-relativistic spin effects vanish, and the modification of the classical dispersion relation is solely associated with the relativistic terms. Several new wave modes appear due the electron spin effects, and an example for astrophysical plasmas are given.
Using nonrelativistic spin quantum fluid theory, parallel propagating electromagnetic waves in electron-positron plasma immersed in a uniform external magnetic field have been investigated. With the inclusion of the spin effect of the plasma species, Faraday rotation appears, which is absent in usual electron-positron plasmas without spin effects. New resonance frequencies and extra cutoffs are observed for both right-hand and left-hand circularly polarized waves.
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