The transition from the classical to the quantum regime in nonlinear Landau damping

Starting from the Wigner-Moyal equation coupled to Poisson's equation, a simplified set of equations describing nonlinear Landau damping of Langmuir waves is derived. This system is studied numerically, with a particular focus on the transition from the classical to the quantum regime. In the quantum regime several new features are found. This includes a quantum modified bounce frequency, and the discovery that bounce-like amplitude oscillations can take place even in the absence of trapped particles. The implications of our results are discussed.