A NOTE ON THE TIME DECAY OF SOLUTIONS FOR THE LINEARIZED WIGNER-POISSON SYSTEM

(Communicated by Pierangelo Marcati) Abstract. We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give an explicit algebraic decay rate. Dedicated to the memory of Marcello Anile 1. Introduction. 1.1. Physical motivation. We consider in a semiclassical framework the dynam-ics of N electrons under the influence of a constant ionic background and their self-consistently generated electrostatic field accounting for mean field effects in the study of quantum plasmas models near admissible stationary states. We are moti