Longitudinal oscillations and linear Landau damping in quark-gluon plasma

On the basis of the semiclassical kinetic Vlasov equation for quark-gluon plasma and the Yang-Mills equation in covariant gauge, linear Landau damping for electrostatic perturbations such as Langmuir waves is investigated for the extreme-relativistic and strongly relativistic cases. It has been observed that for the extreme-relativistic case, wherein the thermal speed of the particles exceeds the phase velocity of the perturbations, the linear Landau damping is absent as has been reported in the literature. However, a departure from extreme-relativistic case generates an imaginary component of the frequency giving rise to linear Landau damping effect. The relevant integral for the conductivity tensor has been evaluated and the dispersion relation for the longitudinal part of the oscillation was obtained. Further, it is also noted that both the real part of the oscillation frequency and the damping rate are sensitive to the choice of the wave number k and the Debye length lambda(D) associated with quark-gluon plasma.