Landau damping and particle trapping in the quantum regime

We review research on electron plasma waves and Landau damping in the quantum regime. Quantum kinetic equations are also briefly reviewed. Particle trapping, harmonic fields, Volkov states in plasmas and other nonlinear effects are discussed. Furthermore, we show that quantum plasma models can be applied to classical plasmas. This includes photon Landau damping and quasiparticle turbulence, with a variety of applications from laser accelerators to space physics, and to particle confinement in magnetic fusion devices. Finally, the case of plasma behaviour in laser-cooled atoms is discussed. We show that the concept of quantum Landau damping is relevant, not only to quantum plasmas, but also to many problems in classical plasmas, and to ultracold matter where plasma models can be applied.