  We consider the application of the original Meyer-Miller (MM) Hamiltonian to
mapping fermionic quantum dynamics to classical equations of motion.
Non-interacting fermionic and bosonic systems share the same one-body density
dynamics when evolving from the same initial many-body state. The MM classical
mapping is exact for non-interacting bosons, and therefore it yields the exact
time-dependent one-body density for non-interacting fermions as well. Starting
from this observation, the MM mapping is compared to different mappings
specific for fermionic systems, namely the spin mapping (SM) with and without
including a Jordan-Wigner transformation, and the Li-Miller mapping (LMM). For
non-interacting systems, the inclusion of fermionic anti-symmetry through the
Jordan-Wigner transform does not lead to any improvement in the performance of
the mappings and instead it worsens the classical description. For an
interacting impurity model and for models of excitonic energy transfer, the MM
and LMM mappings perform similarly, and in some cases the former outperforms
the latter when compared to a full quantum description. The classical mappings
are able to capture interference effects, both constructive and destructive,
that originate from equivalent energy transfer pathways in the models.
