Gravitational collapse in the Schrödinger-Poisson system

Abstract

We perform a quantitative comparison between N-body simulations and the Schrödinger-Poisson system in 1+1 dimensions. In particular, we study halo formation with different initial conditions. We observe the convergence of various observables in the Planck constant $\bar{h}$ and also test virialization. We discuss the generation of higher order cumulants of the particle distribution function which demonstrates that the Schrödinger-Poisson equations should not be perceived as a generalization of the dust model with quantum pressure but rather as one way of sampling the phase space of the Vlasov-Poisson system - just as N-body simulations. Finally, we quantitatively recover the scaling behavior of the halo density profile from N-body simulations