  Out-of-equilibrium systems can host phenomena that transcend the usual
restrictions of equilibrium systems. Here we unveil how out-of-equilibrium
states, prepared via a quantum quench, can exhibit a non-zero Hall-type
response that persists at long times, and even when the instantaneous
Hamiltonian is time reversal symmetric; both these features starkly contrast
with equilibrium Hall currents. Interestingly, the persistent Hall effect
arises from processes beyond those captured by linear response, and is a
signature of the novel dynamics in out-of-equilibrium systems. We propose
quenches in two-band Dirac systems as natural venues to realize persistent Hall
currents, which exist when either mirror or time-reversal symmetry are broken
(before or after the quench). Its long time persistence, as well as sensitivity
to symmetry breaking, allow it to be used as a sensitive diagnostic of the
complex out-equilibrium dynamics readily controlled and probed in cold-atomic
optical lattice experiments.

Quantum Gases;Mesoscale and Nanoscale Physics;Quantum Physics