From magnetized Coulombic quantum dynamics to magnetized fluids

Abstract

We extend the quantum modulated energy developed in [17] in order to de- rive the magnetized pressureless Euler-Poisson equation as a semiclassical and mean field semiclassical limit from the magnetized Schr\"odinger-Poisson and von-Neumann equations, respectively. Local well-posedness of the underlying monokinetic PDE is also addressed. In both limits, the magnetic field is external and may be spatially non-uniform. Our results fall in the broader scope of semiclassical and quantum mean field limits for magnetized quantum dynamics.