  Experimental control over ultracold quantum gases has made it possible to
investigate low-dimensional systems of both bosonic and fermionic atoms. In
closed 1D systems there are a lot of similarities in the dynamics of local
quantities for spinless fermions and strongly interacting "hard-core" bosons,
which on a lattice can be formalised via a Jordan-Wigner transformation. In
this study, we analyse the similarities and differences for spinless fermions
and hard-core bosons on a lattice in the presence of particle loss. The removal
of a single fermion causes differences in local quantities compared with the
bosonic case, because of the different particle exchange symmetry in the two
cases. We identify deterministic and probabilistic signatures of these dynamics
in terms of local particle density, which could be measured in ongoing
experiments with quantum gas microscopes.
