Systematic study of flow of protons and light clusters in intermediate-energy heavy-ion collisions with momentum-dependent potentials

We study the influence of the nuclear equation-of-state (EoS) on collective observables -- the directed ($v_1$) and elliptic flow ($v_2$) of nucleons and light clusters -- in heavy-ion collisions at GeV energies using the Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) approach. A novel development in this work is the inclusion of a momentum-dependent nucleon potential in the PHQMD in addition to the static, density-dependent Skyrme interaction. This enables three distinct EoS scenarios: two static ("soft" and "hard", differing in compressibility) and a soft, momentum-dependent EoS calibrated to $pA$ elastic scattering data. We find a strong EoS sensitivity in proton and cluster rapidity and $p_T$ distributions: soft and soft momentum-dependent EoS yield similar results, markedly different from the hard EoS. Softening the EoS reduces proton yields at midrapidity while enhancing light-cluster production. The EoS also affects flow observables differently for nucleons and clusters. For protons, a soft momentum-dependent potential increases slightly the magnitude of $v_1$ and $v_2$ relative to the hard EoS, whereas cluster flows are nearly similar. The soft momentum-dependent EoS provides an overall good agreement with experimental data from HADES and FOPI Collaborations while the soft EOS is not in line with the data. A scaling of $v_2$ with cluster mass number $A$ is observed at midrapidity for low $p_T$, which breaks at higher $p_T$. Finally, we examine the sensitivity of flow observables to deuteron production mechanisms. Deuterons formed via MST clustering exhibit different flow patterns from those produced by coalescence at freeze-out, indicating that flow harmonics may help discriminate between cluster formation scenarios.