  Dynamics of a system in general depends on its initial state and how the
system is driven, but in many-body systems the memory is usually averaged out
during evolution. Here, interacting quantum systems without external
relaxations are shown to retain long-time memory effects in steady states. To
identify memory effects, we first show quasi-steady state currents form in
finite, isolated Bose and Fermi Hubbard models driven by interaction imbalance
and they become steady-state currents in the thermodynamic limit. By comparing
the steady state currents from different initial states or ramping rates of the
imbalance, long-time memory effects can be quantified. While the memory effects
of initial states are more ubiquitous, the memory effects of switching
protocols are mostly visible in interaction-induced transport in lattices. Our
simulations suggest the systems enter a regime governed by a generalized Fick's
law and memory effects lead to initial-state dependent diffusion coefficients.
We also identify conditions for enhancing memory effects and discuss possible
experimental implications.
