Abstract:
The quantum Vlasov equation has been derived with the use of quasi probability
distribution named as the Wigner function and the electromagnetic Schrodinger
equation. By using this quantum kinetic model the parallel propagating electromagnetic
waves have been studied and the susceptibility tensor for R (right handed
circularly polarized) and L (right handed circularly polarized wave) wave has been
derived. The dispersion relation of R and L waves is obtained by using Fermi Dirac
distribution at zero temperature. By comparing the curves obtained by plotting
quantum dispersion relation of R and L wave with that of the classical R and L
wave, it has been observed that the upper branch of the R wave in quantum plasma
has slightly higher group velocity than that of the R wave in a classical plasma.
While for the lower R wave branch the quantum mechanical group velocity is slower
than the classical group velocity and the anomalous dispersion is observed. Moreover,
the quantum mechanical L wave is almost the same as the classical L wave
but minor corrections are observed at higher values of k which indicates the faster
group velocity of quantum mechanical waves as compared to the classical L wave.
