  Fuzzy Dark Matter (FDM) has recently emerged as an interesting alternative
model to the standard Cold Dark Matter (CDM). In this model, dark matter
consists of very light bosonic particles with quantum mechanical effects on
galactic scales. Using the N-body code AX-GADGET, we perform cosmological
simulations of FDM that fully model the dynamical effects of the quantum
potential throughout cosmic evolution. Through the combined analysis of FDM
volume and high-resolution zoom-in simulations of different FDM particle masses
($m_{\chi}$ $\sim$ $10^{-23} - 10^{-21}$ eV/c$^2$), we study how FDM impacts
the abundance of substructure and the inner density profiles of dark matter
haloes. For the first time, using our FDM volume simulations, we provide a
fitting formula for the FDM-to-CDM subhalo abundance ratio as a function of the
FDM mass.
  More importantly, our simulations clearly demonstrate that there exists an
extended FDM particle mass interval able to reproduce the observed substructure
counts and, at the same time, create substantial cores ($r_{c} \sim 1$ kpc) in
the density profile of dwarf galaxies ($\approx 10^{9}-10^{10}$ M$_{\odot}$),
which stands in stark contrast with CDM predictions even with baryonic effects
taken into account. The dark matter distribution in the faintest galaxies
offers then a clear way to discriminate between FDM and CDM.
