Gravitational collapse in the Schr\"odinger-Poisson system

TL;DR

This paper compares N-body simulations and the Schr"odinger-Poisson system in 1+1 dimensions to study halo formation, convergence of observables, and phase space sampling, providing insights into quantum effects in gravitational collapse.

Contribution

It demonstrates the equivalence of Schr"odinger-Poisson equations and N-body simulations as phase space sampling methods for gravitational collapse.

Findings

Convergence of observables with decreasing Planck constant h-bar.

Successful recovery of halo density profile scaling behavior.

Insights into the role of quantum pressure and phase space sampling.

Abstract

We perform a quantitative comparison between N-body simulations and the Schr\"odinger-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 h-bar and also test virialization. We discuss the generation of higher order cumulants of the particle distribution function which demonstrates that the Schr\"odinger-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.