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 relativistic-quantum analog, however, remains less explored. In this work, we generalize Landau damping to relativistic-quantum regime by analyzing the dynamics of a Klein-Gordon-Poisson (KGP) plasma. We systematically investigate the behavior of the KGP plasma across a parameter space spanned by particle density, temperature, and wave momentum. Our analysis reveals rich structure in the dispersion and damping characteristics. We identify regimes where damping phenomena emerge at relativistic temperature, in Bose-Einstein condensate, and at large momentum recoil. This study provides a unified framework for understanding Landau damping in diverse physical systems and highlights the distinctive features arising in the quantum-relativistic domain.