  Recently, many experiments with cold atomic gases have been conducted from
interest in the non-equilibrium dynamics of correlated quantum systems. Of
these experiments, the mixing dynamics of fermion clusters motivates us to
research cluster-cluster collision dynamics in one-dimensional Fermi systems.
We adopt the one-dimensional Fermi-Hubbard model and apply the time-dependent
density matrix renormalization group method. We simulate collisions between two
fermion clusters of spin-up and spin-down, and calculate reflectance of the
clusters R changing the particle number in each cluster and the interaction
strength between two fermions with up and down spins. We also evaluate the
quasi-classical (independent collision) reflectance R^{qc} to compare it with
R. The quasi-classical picture is quantitatively valid in the limit of weak
interaction, but it is not valid when interaction is strong.
