SpecialityINFN; Università di Parma, IT

Quantum simulation of cold dark matterWe present our numerical methods to integrate time-dependent and nonlinear Schrödinger equations. These include the Gross-Ginsburg-Pitaevskii equation describing ultracold atoms in mean-field approximation and the coupled Schrödinger–Poisson equation system as a model for fuzzy cold dark matter. Despite the success of Wave-like Dark Matter in explaining cosmological processes, its major issue is the high demand in computational resources. Not only does the nonlinear and nonlocal nature of the underlying Schrödinger-Poisson equation pose a problem, but also the range of scales that have to be resolved. We construct two distinct one-dimensional (1+1) toy models that are less expensive from a numerical viewpoint, but still provide analogues to the phenomena observed in three dimensions. Our high-precision numerical technique is tested by an independent basis-function method. Some exemplary results will be shown for two different ways of treating the transverse dimensions, assuming uniform matter distribution in the first and strong confinement - effectively renormalizing the mass or hbar - in the second case. Key features of the asymptotic evolution of artificial and cosmological initial states are presented. Finally, we give an outlook on the future evolution of our numerical techniques towards treating higher spatial dimensions.