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Nonequilibrium models (three-fluid hydrodynamics, UrQMD, and quark molecular dynamics) are used to discuss the uniqueness of often proposed experimental signatures for quark matter formation in relativistic heavy ion collisions from the SPS via RHIC to LHC. It is demonstrated that these models -- although they do treat the most interesting early phase of the collisions quite differently (thermalizing QGP vs. coherent color fields with virtual particles) -- all yield a reasonable agreement with a large variety of the available heavy ion data. Hadron/hyperon yields, including $J/\Psi$ meson production/suppression, strange matter formation, dileptons, and directed flow (bounce-off and squeeze-out) are investigated. Observations of interesting phenomena in dense matter are reported. However, we emphasize the need for systematic future measurements to search for simultaneous irregularities in the excitation functions of several observables in order to come close to pinning the properties of hot, dense QCD matter from data. The role of future experiments with the STAR and ALICE detectors is pointed out., Comment: Proceedings of the Klaus Kinder-Geiger Day

Basic problems of the semiclassical microscopic modelling of strongly interactingsystems are discussed within the framework of Quantum Molecular Dynamics (QMD). This model allows to study the influence of several types of nucleonic interactions on a large variety of observables and phenomena occurring in heavy ion collisions at relativistic energies.It is shown that the same predictions can be obtained with several -- numerically completely different and independently written -- programs as far as the same model parameters are employed and the same basic approximations are made. Many observables are robust against variations of the details of the model assumptions used. Some of the physical results, however, depend also on rather technical parameters like the preparation of the initial configuration in phase space. This crucial problem is connected with the description of the ground state of single nuclei,which differs among the various approaches. An outlook to an improved molecular dynamics scheme for heavy ion collisions is given., Comment: 39 pages, 12 figures

Equilibrium properties of infinite relativistic hadron matter are investigated using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model. The simulations are performed in a box with periodic boundary conditions. Equilibration times depend critically on energy and baryon densities. Energy spectra of various hadronic species are shown to be isotropic and consistent with a single temperature in equilibrium. The variation of energy density versus temperature shows a Hagedorn-like behavior with a limiting temperature of 130$\pm$10 MeV. Comparison of abundances of different particle species to ideal hadron gas model predictions show good agreement only if detailed balance is implemented for all channels. At low energy densities, high mass resonances are not relevant; however, their importance raises with increasing energy density. The relevance of these different conceptual frameworks for any interpretation of experimental data is questioned., Comment: Latex, 20 pages including 6 eps-figures

In this paper, the concepts of microscopic transport theory are introduced and the features and shortcomings of the most commonly used ansatzes are discussed. In particular, the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model is described in great detail. Based on the same principles as QMD and RQMD, it incorporates a vastly extended collision term with full baryon-antibaryon symmetry, 55 baryon and 32 meson species. Isospin is explicitly treated for all hadrons. The range of applicability stretches from $E_{lab}< 100$ MeV/nucleon up to $E_{lab}> 200$ GeV/nucleon, allowing for a consistent calculation of excitation functions from the intermediate energy domain up to ultrarelativistic energies. The main physics topics under discussion are stopping, particle production and collective flow., Comment: 129 pages, pagestyle changed using US letter (8.5x11 in) format. The whole paper (13 Mb ps file) could also be obtained from ftp://ftp.th.physik.uni-frankfurt.de/pub/urqmd/ppnp2.ps.gz

Ratios of hadronic abundances are analyzed for pp and nucleus-nucleus collisions at sqrt(s)=20 GeV using the microscopic transport model UrQMD. Secondary interactions significantly change the primordial hadronic cocktail of the system. A comparison to data shows a strong dependence on rapidity. Without assuming thermal and chemical equilibrium, predicted hadron yields and ratios agree with many of the data, the few observed discrepancies are discussed., Comment: 12 pages, 4 figures

Microscopic calculations of central collisions between heavy nuclei are used to study fragment production and the creation of collective flow. It is shown that the final phase space distributions are compatible with the expectations from a thermally equilibrated source, which in addition exhibits a collective transverse expansion. However, the microscopic analyses of the transient states in the reaction stages of highest density and during the expansion show that the system does not reach global equilibrium. Even if a considerable amount of equilibration is assumed, the connection of the measurable final state to the macroscopic parameters, e.g. the temperature, of the transient ''equilibrium'' state remains ambiguous., Comment: 13 pages, Latex, 8 postscript figures, Proceedings of the Winter Meeting in Nuclear Physics (1997), Bormio (Italy)

The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Dilepton spectra are calculated with and without shifting the $\rho$ pole. Except for S+Au collisions our calculations reproduce the CERES data., Comment: Invited talk at RHIC-theory workshop at BNL july 8-19

The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Effects of a density dependent pole of the $\rho$-meson propagator on dilepton spectra are studied for different systems and centralities at CERN energies., Comment: Proceedings of the Quark Matter '96 Conference, Heidelberg, Germany

Quantum Molecular Dynamics (QMD) calculations of central collisions between heavy nuclei are used to study fragment production and the creation of collective flow. It is shown that the final phase space distributions are compatible with the expectations from a thermally equilibrated source, which in addition exhibits a collective transverse expansion. However, the microscopic analyses of the transient states in the intermediate reaction stages show that the event shapes are more complex and that equilibrium is reached only in very special cases but not in event samples which cover a wide range of impact parameters as it is the case in experiments. The basic features of a new molecular dynamics model (UQMD) for heavy ion collisions from the Fermi energy regime up to the highest presently available energies are outlined., Comment: LaTeX, 12 pages, 8 low-resolution eps-figures, a high resolution PostScript version of the paper is available at http://www.th.physik.uni-frankfurt.de/~konopka/flow.html Invited talk given by H. Stoecker, to appear in the proceedings of the 1st Catania Relativistic Ion Studies (CRIS '96), Catania (Italy), May 27-31 1996

We study the thermodynamic properties of infinite nuclear matter with the Ultrarelativistic Quantum Molecular Dynamics (URQMD), a semiclassical transport model, running in a box with periodic boundary conditions. It appears that the energy density rises faster than $T^4$ at high temperatures of $T\approx 200-300$~MeV. This indicates an increase in the number of degrees of freedom. Moreover, We have calculated direct photon production in Pb+Pb collisions at 160~GeV/u within this model. The direct photon slope from the microscopic calculation equals that from a hydrodynamical calculation without a phase transition in the equation of state of the photon source., Comment: Proceedings of the XIV International Conference on Particles and Nuclei (PANIC'96), 22-28 May 1996, Williamsburg, Virginia, USA, to be published by World Scientific Publ. Co. (3 pages)

The microscopic phasespace approach URQMD is used to investigate the stopping power and particle production in heavy systems at SPS and RHIC energies. This framework bridges with one model consistently the entire available range of energies from below SIS to CERN, even for the heaviest system Pb+Pb. URQMD is a hadronic transport model based on the propagation of hadrons on classical trajectories in the framework of Lorentz-invariant dynamics. It includes secondary interactions e.g. annihilation of produced mesons leading to the formation of resonances and the excitation of strings. The collision term contains 50 different baryon species (including nucleon, delta and hyperon resonances with masses up to 2 GeV) and 25 different meson species (including strange meson resonances), which are supplemented by their corresponding antiparticle and all isospin-projected states. Within this approach we find no gap in the baryon rapidity distribution even at RHIC. For CERN (SPS) energies URQMD shows a pile up of baryons and a supression of multi-nucleon clusters (e.g. He) at midrapidity., Comment: Proc. Int. Conf. on Nuclear Physics at the Turn of the Millenium: Structure of Vacuum and Elementary Matter, 10-16 March 1996, Wilderness/George, South Africa