Dynamical resistivity of a few interacting fermions to the time-dependent potential barrier

We study the dynamical response of a harmonically trapped two-component few-fermion mixture to the external Gaussian potential barrier moving across the system. The simultaneous role played by inter-particle interactions, rapidity of the barrier, and the fermionic statistics is explored for systems containing up to four particles. The response is quantified in terms of the temporal fidelity of the time-evolved state and the amount of quantum correlations between components being dynamically generated. Results are also supported by analysis of the single-particle densities and temporal number of occupied many-body eigenstates. In this way, we show that the dynamical properties of the system crucially depend on non-trivial mutual relations between temporal many-body eigenstates, and in consequence, they lead to volatility of the dynamics. Counterintuitively, imbalanced systems manifest much higher resistivity and stability than their balanced counterparts.