Quantum aspects of hydrodynamic transport from weak electron-impurity scattering

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, the understanding of the observed nonlocal 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 nonlocal conductivity effects such as those observed in experiments because of the fermionic system's long-range entangled nature. On the basis of explicit calculations of the conductivity at finite wave vector, $\ensuremath{\sigma}(\mathbf{q})$, for selected weakly disordered free-fermion systems, we propose experimental strategies for demonstrating distinctive quantum effects in nonlocal 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.