Extracting the equation of state from a microscopic non-equilibrium model

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

Microscopic Analysis of Thermodynamic Parameters from 160 MeV/n - 160 GeV/n

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

Microscopic Models for Ultrarelativistic Heavy Ion Collisions

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 $E_{lab} 200$ 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.g

Signatures of dense hadronic matter in ultrarelativistic heavy ion reactions

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 8-1

Transition to resonance-rich matter in heavy ion collisions at RHIC energies

The equilibration of hot and dense nuclear matter produced in the central region in central Au+Au collisions at $\sqrt{s}=200$ AGeV is studied within the microscopic transport model UrQMD. The pressure here becomes isotropic at $t \approx 5$ fm/c. Within the next 15 fm/c the expansion of the matter proceeds almost isentropically with the entropy per baryon ratio $S/A \approx 150$. During this period the equation of state in the $(P,\epsilon)$-plane has a very simple form, $P=0.15 \epsilon$. Comparison with the statistical model (SM) of an ideal hadron gas reveals that the time of $\approx 20$ fm/$c$ may be too short to attain the fully equilibrated state. Particularly, the fractions of resonances are overpopulated in contrast to the SM values. The creation of such a long-lived resonance-rich state slows down the relaxation to chemical equilibrium and can be detected experimentally.Comment: Talk at the conference Strangeness'2000, to be published in J. of Phys.

Local Thermal and Chemical Equilibration and the Equation of State in Relativistic Heavy Ion Collisions

Thermodynamical variables and their time evolution are studied for central relativistic heavy ion collisions from 10.7 to 160 AGeV in the microscopic Ultrarelativistic Quantum Molecular Dynamics model (UrQMD). The UrQMD model exhibits drastic deviations from equilibrium during the early high density phase of the collision. Local thermal and chemical equilibration of the hadronic matter seems to be established only at later stages of the quasi- isentropic expansion in the central reaction cell with volume 125 fm$^{3}$. distributions at all collision energies for $t\geq 10 fm/c$ with a unique Baryon energy spectra in this cell are approximately reproduced by Boltzmann rapidly dropping temperature. At these times the equation of state has a simple form: $P \cong (0.12-0.15) \epsilon$. At 160 AGeV the strong deviation from chemical equilibrium is found for mesons, especially for pions, even at the late stage of the reaction. The final enhancement of pions is supported by experimental data.Comment: 17 Pages, LaTex, 8 eps figures. Talk given at SQM'98 conference, 20-24 July 1998, Padova, Italy, submitted to J. Phys.

Microscopic calculations of stopping and flow from 160AMeV to 160AGeV

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, German

Equation of state of resonance-rich matter in the central cell in heavy-ion collisions at s\sqrt{s}=200 AGeV

The equilibration of hot and dense nuclear matter produced in the central cell of central Au+Au collisions at RHIC ($\sqrt{s}=200$ AGeV) energies is studied within a microscopic transport model. The pressure in the cell becomes isotropic at $t\approx 5$ fm/$c$ after beginning of the collision. Within the next 15 fm/$c$ the expansion of matter in the cell proceeds almost isentropically with the entropy per baryon ratio $S/A \approx 150$, and the equation of state in the $(P,\epsilon)$ plane has a very simple form, $P=0.15\epsilon$. Comparison with the statistical model of an ideal hadron gas indicates that the time $t \approx 20$ fm/c may be too short to reach the fully equilibrated state. Particularly, the creation of long-lived resonance-rich matter in the cell decelerates the relaxation to chemical equilibrium. This resonance-abundant state can be detected experimentally after the thermal freeze-out of particles.Comment: LATEX, 21 pages incl. 7 figure