Landau Damping in Klein-Gordon-Poisson plasma

Landau damping, a cornerstone in classical plasma physics, describes the decay of electrostatic waves due to wave-particle interactions. Its quantum analog, however, remains less explored. In this study, we aim to generalize Landau damping from classical plasma to quantum plasma described by the Klein-Gordon equation, which reduces to the Vlasov equation in classical limits. By coupling with Poisson's equation, we systematically derive the normal modes of the system. Subsequently, we extend the analysis to understand collisionless damping mechanisms for each mode, drawing parallels with Landau's classical treatment. Our findings reveal that quantum Landau damping possesses features not present in classical settings. Our work develops a quantum description of wave-particle interactions and advances our understanding of damping phenomena in quantum plasmas.