Quantum Methodologies in Beam, Fluid and Plasma Physics

The quantum methodologies useful for describing in a unified way several problems of nonlinear and collective dynamics of fluids, plasmas and beams are presented. In particular, the pictures given by the Madelung fluid and the Moyal-Ville-Wigner phase-space quasidistribution, including the related quantum tools such as marginal distributions for the tomographic representations, are described. Some relevant applications to soliton and modulational instability theory are presented.