  Discrete time-crystals are periodically driven quantum many-body systems with
broken discrete-time translational symmetry, a non-equilibrium steady state
representing self-organization of motion of quantum particles. Observations of
discrete time-crystalline order are currently limited to magneto-optical
experiments. Crucially, it was never observed in a transport experiment
performed on systems connected to external electrodes. Here we demonstrate that
both discrete time-crystal and quasi-crystal survive a very general class of
environment corresponding to single-particle gain and loss through
system-electrode coupling over experimentally relevant timescales. Using
dynamical symmetries, we analytically identify the conditions for observing
time-crystalline behavior in a periodically driven open Fermi-Hubbard chain
attached to electrodes. Remarkably, the spin-polarized transport current
directly manifests the existence of a time-crystalline behavior. Our findings
are verifiable in present-day experiments with quantum-dot arrays and Fermionic
ultra-cold atoms in optical lattices.
