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A consideration of waves propagating parallel to the external magnetic fieldis presented. The dielectric permeability tensor is derived from quantumkinetic equations with non-trivial equilibrium spin-distribution functions(NTESDF) in the linear approximation on amplitude of wave perturbations. Ingeneral case, x- and y-projections of the SDF are nonzero which is called thenon-trivial regime. Corresponding equilibrium solution is found. Contributionof the NTESDF appears in the dielectric permeability tensor in the additiveform. It is explicitly found here. Corresponding modification in the dispersionequation for the transverse waves is derived. Contribution of NTESDF in thespectrum of transverse waves is calculated numerically. It is found that theterm caused by the NTESDF can be comparable with the classic terms for therelatively small wave vectors and frequencies above the cyclotron frequency. Inmajority of regimes, the extra spin caused term dominates over the spin termfound earlier, except the small frequency regime, where their contributions inthe whistler spectrum are comparable. A decrease of the left-hand circularlypolarized wave frequency, an increase of the high-frequency right-handcircularly polarized wave frequency, and a decrease of frequency changing by anincrease of frequency at the growth of the wave vector for the whistler arefound. A dramatic decrease of the spin wave frequency resulting in severaltimes larger group velocity of the spin wave is found either. Found dispersionequations are used for obtaining of an effective quantum hydrodynamicsreproducing these results. This generalization requires the introduction ofcorresponding equation of state for the thermal part of the spin current in thespin evolution equation.

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