  Recent experimental observations of apparently hydrodynamic electronic
transport have generated much excitement. However, the understanding of the
observed non-local transport (whirlpool) effects and parabolic
(Poiseuille-like) current profiles has largely been motivated by a
phenomenological analogy to classical fluids. This is due to difficulty in
incorporating strong correlations in quantum mechanical calculation of
transport, which has been the primary angle for interpreting the apparently
hydrodynamic transport. Here we demonstrate that even free fermion systems, in
the presence of (inevitable) disorder, exhibit non-local conductivity effects
such as those observed in experiment because of the fermionic system's
long-range entangled nature. On the basis of explicit calculations of the
conductivity at finite wavevector, $\sigma({\bf q})$, for selected weakly
disordered free fermion systems, we propose experimental strategies for
demonstrating distinctive quantum effects in non-local transport at odds with
the expectations of classical kinetic theory. Our results imply that the
observation of whirlpools or other "hydrodynamic" effects does not guarantee
the dominance of electron-electron scattering over electron-impurity
scattering.
