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Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) -- A Novel Microscopic N-Body Transport Approach for Heavy-Ion Collisions, Dynamical Cluster Formation and Hypernuclei Production

Cluster and hypernuclei production in heavy-ion collisions is presently under active experimental and theoretical investigation. Since clusters are weekly bound objects, their production is very sensitive to the dynamical evolution of the system and its interactions. The theoretical description of cluster formation is related to the n-body problem. Here we present the novel n-body dynamical transport approach PHQMD (Parton-Hadron-Quantum-Molecular Dynamics) which is designed to provide a microscopic description of nuclear cluster and hypernucleus formation as well as of general particle production in heavy-ion reactions at relativistic energies. In difference to the coalescence or statistical models, often used for the cluster formation, in PHQMD clusters are formed dynamically due to the interactions between baryons described on a basis of Quantum Molecular Dynamics (QMD)which allows to propagate the n-body Wigner density and n-body correlations in phase-space, essential for the cluster formation. The clusters are identified by the MST (Minimum Spanning Tree) or the SACA ('Simulated Annealing Cluster Algorithm') algorithm which finds the most bound configuration of nucleons and clusters. Collisions among hadrons as well as Quark-Gluon-Plasma formation and parton dynamics in PHQMD are treated in the same way as in the established PHSD (Parton-Hadron-String Dynamics)transport approach. In order to verify our approach with respect to the general dynamics we present here the first PHQMD results for general 'bulk' observables such as rapidity distributions and transverse mass spectra for hadrons ($π, K, \bar K, p, \bar p, Λ, \bar Λ$) from SIS to RHIC energies. We find a good description of the 'bulk' dynamics which allows us to proceed with the results on cluster production, including hypernuclei.