Search

A wealth of data on charmonium production in Pb-Pb collisions from the LHC experiments has provided strong evidence for (re-)generation as a dominant production mechanism at low transverse momentum. We present an important extension of the statistical hadronisation model to describe $\rm{J}/\psi$ transverse momentum distributions based on input parameters from hydrodynamical simulations. Comparison to the data allows the testing of the degree of thermalisation of charm quarks in the quark-gluon plasma. To this end we will report analyses of the $\rm{J}/\psi$ transverse momentum spectra in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ and $5.02$ TeV., Comment: 4 pages, 4 figures, proceedings for Quark Matter 2018, Venice, Italy

In a quantum field theory, apparent thermalization can be a consequence of entanglement as opposed to scatterings. We discuss here how this can help to explain open puzzles such as the success of thermal models in electron-positron collisions. It turns out that an expanding relativistic string described by the Schwinger model (which also underlies the Lund model) has at early times an entanglement entropy that is extensive in rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature $T_\tau=\hbar/(2\pi k_B\tau)$, even in the absence of any scatterings., Comment: Contribution to the proceedings of Quark Matter 2018, to appear in Nuclear Physics A

The field of jet quenching studies is witnessing an interesting development marked by the appearance of jet sub-structure observables. I give my personal view on this class of observables and comment on how they are connected to thermalisation.

Due to their large masses, heavy quarks are predominantly produced through initial hard scatterings in heavy-ion collisions and, as such, they experience the entire evolution of the hot and dense medium created in those collisions. They can therefore provide important insights into the properties of the strongly-coupled Quark-Gluon Plasma. For instance, the measurement of the elliptic flow ( v 2 ) of charm quarks can provide information on the degree of thermalization for charm quarks in the medium and thus the bulk properties of the system. Furthermore, several models have predicted that fluctuations in the initial conditions, together with strong charm-medium interactions, could lead to a finite triangular flow ( v 3 ) for charm quarks, providing another handle to study the dynamics at the early stage of heavy-ion collisions. In these proceedings, we present the measurements of the v 2 and v 3 of D 0 mesons in Au+Au collisions at s NN = 200 GeV with the Heavy Flavor Tracker at STAR. Compared to previously reported D 0 v 2 in minimum-bias collisions, the precision of the new results is improved by a factor of 2–4 depending on D 0 transverse momentum ( p T ). The D 0 v 3 as a function of p T is also reported for the first time. The results are compared with the measurements of other particle species and a series of model calculations.

Arguments for thermalization of the QCD matter created in high-energy nuclear collisions has dominantly come from the agreement of the measured yields of produced hadrons with those from statistical thermal models. Ideally for a thermalized system, in addition to mean, the higher orders of the moments of the multiplicity distribution of produced particles should also show agreement with thermal models. In this respect, simultaneously studying the moments of the event-by-event distributions of conserved quantities like net-baryon, net-strangeness and net-charge number is best suited. We present a systematic study of comparing the results from a thermal hadron resonance gas (HRG) model with data on higher moments of net-proton, net-kaon and net-charge distributions measured at RHIC beam energy scan program. The experimental acceptances in terms of rapidity and transverse momentum are used in the model calculations which also include resonance decay. For the first time, the HRG model results are found to explain the measurements up to third order of moment with a common temperature and baryonic chemical potential. These calculations have tested the thermal nature of produced net-particle distributions up to third order, thereby providing evidence for thermalization of the QCD matter formed in such high energy heavy-ion collisions.

Chaos against thermalization, which was earlier investigated in the sd-shell space, is examined in the f5p-shell space. The two-body residual interaction of f5pvh with realistic single-particle energies have been utilized for carrying out f5p-shell space calculations. The present study demonstrates that the spectral fluctuations computed with realistic single-particle energies are in accordance with the Gaussian orthogonal ensemble of random matrices. Besides, the equilibrium heating is extremely related with the progress of many-body quantum chaos. Moreover, the single-particle entropy of individual states in the mean field basis is dissimilar to the thermodynamic entropy determined from the level density. The present results, which are a check of the ideas of many-body quantum chaos in a different version of the nuclear shell model applied to another part of the periodic table, are fully confirming what was formerly achieved in the sd-shell space and in this way exhibit their generality.

We have studied by means of kinetic theory based on a relativistic Boltzmann-like transport simulation the impact of the out-of-equilibrium initial distribution proper of a Color Glass Condensate into the build-up the elliptic flow. Our main result is that the available data on v 2 are in agreement with a η / s ≈ 1 / 4 π also for Color Glass Condensate initial conditions. We have found that the impact of the nonequilibrium implied by the saturation scale can modify the estimate of the viscosity respect to the assumption of full thermalization in p T -space. In particular we have observed that the estimate of η / s is modified from η / s ≈ 2 / 4 π to η / s ≈ 1 / 4 π at RHIC and from η / s ≈ 3 / 4 π to η / s ≈ 2 / 4 π at LHC

A general overview on the role of heavy quarks as probes of the medium formed in high energy nuclear collisions is presented. Experimental data compared to model calculations at low and moderate pT are exploited to extract information on the transport coefficients of the medium, on possible modifications of heavy flavor hadronization in a hot environment and to provide quantitative answers to the issue of kinetic (and chemical, at conceivable future experimental facilities) thermalization of charm. Finally, the role of heavy flavor at high pT as a tool to study the mass and color-charge dependence the jet quenching is also analyzed., Quark Matter 2014 proceedings

I give a brief introduction to the AdS/CFT correspondence targeted at heavy-ion physicists. I also review some insights to our understanding of the early stages of heavy-ion collisions coming from selected studies made using methods of the AdS/CFT correspondence., 8 pages, 4 figures. Plenary talk at the Quark Matter 2014 conference

One of the unsolved problems in the current 'standard model' of heavy ion physics is the apparent rapid thermalization of QCD matter in the pre-equilibrium stage. While it is challenging to probe this mechanism directly, there are now several observables available which allow tomographic imaging of the initial state geometry, which is expected to carry remnant information of the equilibration mechanism. On the fluid dynamics side, scaled fluctuations in the momentum space anisotropy parameters v_n image the initial eccentricity fluctuations epsilon_n almost directly with only a weak dependence on the details of the fluid dynamical evolution. From a different direction, due to the strong non-linear dependence of their emission rates on temperature, thermal photons and their v_n are very sensitive to the initial state graininess. Finally, the v_2 and v_3 of high P_T hadrons coming from hard processes reflect the attenuation pattern of partons propagating through the inhomogeneous matter density after some fluid dynamical evolution. Combining information from all these channels does not yet lead to a fully consistent picture, however intriguing trends pointing towards non-trivial initial state dynamics emerge., 4 pages, talk given at the XXIV International Conference on uktrarelativistic Nucleus Nucleus Collisions (Quark Matter 2014), 19-24 May, Darmstadt, Germany

We discuss the onset of the thermalization process in high-energy heavy-ion collisions from a weak coupling perspective, using classical-statistical real-time lattice simulations as a first principles tool to study the pre-equilibrium dynamics. Most remarkably, we find that the thermalization process is governed by a universal attractor, where the space-time evolution of the plasma becomes independent of the initial conditions and exhibits the self-similar dynamics characteristic of wave turbulence. We discuss the consequences of our weak coupling results for the thermalization process in heavy-ion experiments and briefly comment on the use of weak coupling techniques at larger values of the coupling., Comment: Proceedings for Quark Matter 2014, Darmstadt (Germany), May 19-24, 2014

The early time behavior of heavy ion collisions involves new forms of matter such as the Color Glass Condensate and the Glasma. An area of much recent work involves attempts to understand the development of the Glasma into a thermalized Quark Gluon Plasma. The evolution of the Glasma involves turbulent Yang–Mills fields, and might also have condensates and non-trivial topological excitations. The proton–nucleus collision experiments at the LHC accelerator may provide unique insight into these forms of matter and the role they play at various times in hadronic collisions. I introduce and review aspects of these forms of matter as related to experiments at the LHC and RHIC accelerators.

J/ suppression induced by color screening of its constituent quarks was proposed 26 years ago as a signature of the formation of a quark gluon plasma in heavy-ion collisions. Recent results from ALICE in Pb-Pb collisions exhibit a smaller suppression with respect to previous measurements at the SPS and RHIC. The study of azimuthal anisotropy in particle production gives information on the collective hydrodynamic expansion at the early stage of the fireball, where the matter created in high-energy nuclear collisions is expected to be in a deconfined state. In particular, J/ elliptic flow v2 is important to test the degree of thermalization of heavy quarks. Together with the production yields, the elliptic flow is a powerful observable to address the question of suppression and regeneration of J/ in QGP. We present the first inclusive J/ elliptic flow measurement performed with the muon spectrometer of ALICE, in Pb-Pb collisions, at forward rapidity. Integrated and pT-di erential v2 results are presented and a comparison with recent STAR results and with a parton transport model is also performed.

We studied thermalization of strongly coupled gauge theory using a gravitational collapse model. In particular, we studied unequal time correlator for the glue ball operator. We found singularities of the correlator for zero momentum sector is consistent with a geometric optics picture in the gravitational theory. The singularities of the correlator indicates strong temporal correlation, thus the time after which the singularities disappear provides a measure of the temporal decoherence in the thermalization process.

We report recent progress on understanding the thermalization of the quark-gluon plasma during the early stage in a heavy ion collision. The initially high overpopulation in the far-from-equilibrium gluonic matter ("Glasma") is shown to play a crucial role. The strongly interacting nature (and thus fast evolution) naturally arises as an {\em emergent property} of this pre-equilibrium matter where the intrinsic coupling is weak but the highly occupied gluon states coherently amplify the scattering. A possible transient Bose-Einstein Condensate is argued to form dynamically on a rather general ground. We develop a kinetic approach for describing its evolution toward thermalization, and based on that we find approximate scaling solutions as well as numerically study the onset of condensation., Comment: 4 pages, 3 figures. Contribution to the proceedings of Quark Matter 2012, August 13-18, 2012, Washington DC

We review the Color Glass Condensate effective theory, that describes the gluon content of a high energy hadron or nucleus, in the saturation regime. The emphasis is put on applications to high energy heavy ion collisions. After describing initial state factorization, we discuss the Glasma phase, that precedes the formation of an equilibrated quark-gluon plasma. We end this review with a presentation of recent developments in the study of the isotropization and thermalization of the quark-gluon plasma., Invited review for International Journal of Modern Physics; based on lectures given at the 22nd Jyvaskyla Summer School, August 2012; 55 pages; v2: some extra references

Hydrodynamical models have generally failed to describe interferometry radii measured at RHIC. In order to investigate this ``HBT puzzle'', we carry out a systematic study of HBT radii in ultrarelativistic heavy-ion collisions within a two-dimensional transport model. We compute the transverse radii $R_o$ and $R_s$ as functions of $p_t$ for various values of the Knudsen number, which measures the degree of thermalization in the system. For realistic values of the Knudsen number estimated from $v_2$ data, we obtain $R_o/R_s \simeq 1.2$, much closer to data than standard hydrodynamical results. Femtoscopic observables vary little with the degree of thermalization. Azimuthal oscillations of the radii in non central collisions do not provide a good probe of thermalization., Comment: Proceedings for Quark Matter 2009, Knoxville, TN USA

Using the AdS/CFT correspondence, we compute the medium-induced energy loss of a decelerating heavy quark moving through a strongly-coupled supersymmetric Yang Mills plasma. In the regime where the deceleration is small, a perturbative calculation is possible and we obtain the first two corrections to the energy-loss rate of a heavy quark with constant velocity. The thermalization of the heavy quark is also discussed., 4 pages, no figures, Proceedings of the 21st International Conference on Ultra-Relativistic Nucleus Nucleus Collisions (QM09), Knoxville, USA, March 30-April 4 2009

A homogeneous color magnetic field is known to be unstable for the fluctuations perpendicular to the field in the color space (the Nielsen-Olesen instability). We argue that these unstable modes, exponentially growing, generate an azimuthal magnetic field with the original field being in the z-direction, which causes the Nielsen-Olesen instability for another type of fluctuations. The growth rate of the latter unstable mode increases with the momentum p_z and can become larger than the former's growth rate which decreases with increasing p_z. These features may explain the interplay between the primary and secondary instabilities observed in the real-time simulation of a non-expanding glasma, i.e., stochastically generated anisotropic Yang-Mills fields without expansion., Comment: 18 pages, 4 figures (minor revision)

We treat a gas of interacting relativistic effective mesons (similar to those produced in a heavy-ion collision), regarded as a nonequilibrium statistical system. The large number of degrees of freedom gives rise to statistical features. We suppose large occupation numbers, temperature somewhat below typical critical temperatures and the quasi-classical regime. At the initial time t0, the gas is off-equilibrium. We analyze the time evolution of the quasi-classical effective meson gas for t > t 0 by using a new moment method. Long-time approximations, which could yield the approach to global thermal equilibrium, are presented.

This work calculates the first correction to the leading order q\={q} dilepton production rates due to shear viscosity in an expanding gas. The modified rates are integrated over the space-time history of a viscous hydrodynamic simulation of RHIC collisions. The net result is a {\em hardening} of $q_\perp$ spectrum with the magnitude of the correction increasing with invariant mass. We argue that a thermal description is reliable for invariant masses less than $M_{max}\approx(2\tau_0 T_0^2)/(\eta/s)$. For reasonable values of the shear viscosity and thermalization time $M_{max}\approx 4.5$ GeV. Finally, the early emission from a viscous medium is compared to emission from a longitudinally free streaming plasma. Qualitative differences in $q_\perp$ spectrum are seen which could be used to extract information on the thermalization time, viscosity to entropy ratio and possibly the thermalization mechanism in heavy-ion collisions., Comment: 17 pages, 8 figures

Recent results on chemical freeze-out and multi-strange hadron transverse momentum distributions are discussed and compared with model predictions. The idea of heavy flavor collectivity and light flavor thermalization is presented in the light of recent heavy flavor measurement at RHIC.

I argue that the physics of the scattering of very high energy strongly interacting particles is controlled by a new, universal form of matter, the Color Glass Condensate. This matter is the dominant contribution to the low x part of a hadron wavefunction. In collisions, this mater almost instantaneously turns into a Glasma. The Glasma initially has strong longitudinal color electric and magnetic fields, with topological charge. These fields melt into gluons. Due to instabilities, quantum noise is converted into classical turbulence, which may be responsible for the early thermalization seen in heavy ion at RHIC

Within a pQCD inspired kinetic parton cascade we simulate the space time evolution of gluons which are produced initially in a heavy ion collision at RHIC energy. The inelastic gluonic interactions gg ↔ ggg do play an important role: For various initial conditions it is found that thermalization and the close to ideal fluid dynamical behaviour sets in at very early times. Special emphasis is put on color glass condensate initial conditions and the 'bottom up thermalization' scenario. Off-equilibrium 3 → 2 processes make up the very beginning of the evolution leading to an initial decrease in gluon number and a temporary avalanche of the gluon momentum distribution to higher transversal momenta.

Thermalization and collective flow of charm (c) and bottom (b) quarks are evaluated from elastic parton scattering via "D"- and "B"-meson resonances in an expanding, strongly interacting quark-gluon plasma at RHIC. Pertinent drag and diffusion coefficients are implemented into a relativistic Langevin simulation to compute transverse-momentum spectra and azimuthal flow asymmetries (v_2) of c- and b-quarks. Upon hadronization (including coalescence and fragmentation) and semileptonic D- and B-decays, the resulting electron spectra (R_{AA} and v_2) are compared to recent RHIC data., 4 pages, 4 figures, proceedings for Quark Matter 2005; v2: Acknowledgment added

A new thermalization scenario for heavy ion collisions is discussed. It is based on the Hawking--Unruh effect: an observer moving with an acceleration $a$ experiences the influence of a thermal bath with an effective temperature $T = a / 2\pi$, similar to the one present in the vicinity of a black hole horizon. In the case of heavy ion collisions, the acceleration is caused by a pulse of chromo--electric field $E \sim Q_s^2/g$ ($Q_s$ is the saturation scale, and $g$ is the strong coupling), the typical acceleration is $a \sim Q_s$, and the heat bath temperature is $T \simeq Q_s / 2\pi \sim 200$ MeV. In nuclear collisions at sufficiently high energies the effect can induce a rapid thermalization over the time period of $\tau \sim \pi/Q_s $ accompanied by phase transitions. A specific example of chiral symmetry restoration induced by the chromo--electric field is considered; it is mathematically analogous to the phase transition occurring in the vicinity of a black hole., Comment: 10 pages, 2 figures, based on invited talks given at the "Quark Matter 2005" Conference, Budapest, Hungary, 4-9 August 2005, and Workshop on "Quark-Gluon Plasma Thermalization", Vienna, Austria, 10-12 August 2005

We discuss a model for the energy distribution and the early space-time evolution of a heavy ion collision. We estimate the gluon field generated in the wake of hard processes and through primordial fluctuations of the color charges in the nuclei. Without specifying the dynamical mechanism of thermalization we calculate the energy momentum tensor of the following plasma phase. The results of this model can be used as initial conditions for a further hydrodynamic evolution., Contribution to Quark Matter 2005; 4 pages, 4 figures

We argue that isotropization and, consequently, thermalization of the system of gluons and quarks produced in an ultrarelativistic heavy ion collision does not follow from Feynman diagram analysis to all orders in the coupling constant. We conclude that the apparent thermalization of quarks and gluons, leading to success of Bjorken hydrodynamics in describing heavy ion collisions at RHIC, can only be attributed to the non-perturbative QCD effects not captured by Feynman diagrams.

We start by presenting physical arguments for the impossibility of perturbative thermalization leading to (non-viscous) Bjorken hydrodynamic description of heavy ion collisions. These arguments are complimentary to our more formal argument presented in [hep-ph/0503038]. We argue that the success of hydrodynamic models in describing the quark-gluon system produced in heavy ion collisions could only be due to non-perturbative strong coupling effects. We continue by studying non-perturbative effects in heavy ion collisions at high energies. We model non-perturbative phenomena by an instanton ensemble. We show that non-perturbative instanton vacuum fields may significantly contribute to jet quenching in nuclear collisions. At the same time, the instanton ensemble contribution to thermalization is likely to be rather weak, leading to non-perturbative thermalization time comparable to the time of hadronization. This example illustrates that jet quenching is not necessarily a signal of a thermalized medium. Indeed, since the instanton models do not capture all the effects of QCD vacuum (e.g. they do not account for confinement), there may be other non-perturbative effects facilitating thermalization of the system., 26 pages, no figures

Triple-gluon scattering processes in gluon matter initially created in Au–Au collisions at RHIC energies become important. The three-gluon scatterings are calculated in perturbative QCD and give rise to a new term in a transport equation for gluon distribution. A numerical solution of the transport equation demonstrates gluon momentum isotropy achieved at a time of the order of 0.65 fm/ c and can thus be fitted to a thermal distribution with fugacity of 0.065 and temperature of 0.75 GeV. Triple-gluon scatterings lead to a short thermalization time of gluon matter.

It is shown that recent RHIC data on hadron spectra and elliptic flow can be excellently reproduced within a hydrodynamic description of the collision dynamics, and that this provides strong evidence for rapid thermalization while the system is still in the quark-gluon plasma phase. But even though the hydrodynamic approach provides an impressive description of the single-particle momentum distributions, it fails to describe the two-particle momentum correlation (HBT) data for central Au+Au collisions at RHIC. We suggest that this is not likely to be repaired by further improvements in our understanding of the early collision stages, but probably requires a better modelling of the freeze-out process. We close with a prediction of the phases of the azimuthal oscillations of the HBT radii in noncentral collisions at RHIC., Comment: 12 pages, including 6 figures. Invited talk at the International Conference on "Statistical QCD", Bielefeld, August 26-30, 2001, to appear in the proceedings (F. Karsch and H. Satz, eds.) in Nucl. Phys. A

In this talk I describe how thermalization occurs in heavy-ion collisions in the asymptotically weak coupling regime, and how it is related to parton energy loss.

We report the elliptic flow of charged and identified particles at mid-rapidity in Au+Au collisions at $\sqrt{s_{_{NN}}}=130$ GeV using the STAR TPC at RHIC. The integrated elliptic flow signal, $v_2$, for charged particles reaches values of about 0.06, indicating a higher degree of thermalization than at lower energies. The differential elliptic flow signal, $v_2$($p_t$) up to 1.5 GeV/$c$, shows a behavior expected from hydrodynamic model calculations. Above 1.5 GeV/$c$, the data deviate from the hydro predictions; however the $v_2$($p_t$) is still large, suggesting finite asymmetry for the products of hard scattering. For the identified particles, elliptic flow as a function of $p_t$ and centrality differ significantly for particles of different masses. This dependence can be accounted for in hydrodynamic models, indicating that the system created shows a behavior consistent with collective hydrodynamical flow.

In this paper, we study the thermalization of gluons and N_f flavors of massless quarks and antiquarks in a spatially homogeneous system. First, two coupled transport equations for gluons and quarks (and antiquarks) are derived within the diffusion approximation of the Boltzmann equation, with only 2 2 processes included in the collision term. Then, these transport equations are solved numerically in order to study the thermalization of the quark-gluon plasma. At initial time, we assume that no quarks or antiquarks are present and we choose the gluon distribution in the form f = f_0 theta (1-p/Q_s) with Q_s the saturation momentum and f_0 a constant. The subsequent evolution of systems may, or may not, lead to the formation of a (transient) Bose condensate, depending on the value of f_0. In fact, we observe, depending on the value of f_0, three different patterns: (a) thermalization without gluon Bose-Einstein condensate (BEC) for f_0 < f_{0t}, (b) thermalization with transient BEC for f_{0t} < f_0 < f_{0c}, and (c) thermalization with BEC for f_{0c} < f_0. The values of f_{0t} and f_{0c} depend on N_f. When f_0> 1 > f_{0c}, the onset of BEC occurs at a finite time t_c ~ 1/((alpha_s f_0)^2 Q_s). We also find that quark production slows down the thermalization process: the equilibration time for N_f = 3 is typically about 5 to 6 times longer than that for N_f = 0 at the same Q_s., 32 pages, 25 figures, minor modifications, Final version published in NPA

We present a three source analysis of velocity spectra of light charged particles (LCP) and neutrons emitted in the reaction 40 Ar+ 27 Al at 44 A MeV . The light particle (LP) velocity spectra are studied as a function of the detection angle (1.5° θ 3 He, 4 He, d , t ratios and the PLF proton temperature parameter. The characteristics of the PLF sources are derived. Present results are discussed with regards to the degree of thermalization which could be achieved in the PLF and TLF sources.

A radiative transport model is used to study kinetic equilibration during the early stage of a relativistic heavy ion collision. The parton system is found to be able to overcome expansion and move toward thermalization via parton collisions. Scaling behaviors show up in both the pressure anisotropy and the energy density evolutions. In particular, the pressure anisotropy evolution shows an approximate alpha_s scaling when radiative processes are included. It approaches an asymptotic time evolution on a time scale of 1 to 2 fm/c. The energy density evolution shows an asymptotic time evolution that decreases slower than the ideal hydro evolution. These observations indicate that partial thermalization can be achieved and viscosity is important for the evolution during the early longitudinal expansion stage of a relativistic heavy ion collision., Presented at the 10th International Conference on Nucleus-Nucleus Collisions (NN2009), Beijing, China, 16-21 Aug 2009

The second and fourth Fourier harmonics of the azimuthal distribution of particles, v 2 and v 4 , have been mesured in Au-Au collisions at the Relativistic Heavy Ion Collider (RHIC). The ratio v 4 / ( v 2 ) 2 is significantly larger than predicted by hydrodynamics. Effects of partial thermalization are estimated on the basis of a transport calculation, and are shown to increase the ratio by a small amount. We argue that the large value of v 4 / ( v 2 ) 2 seen experimentally is mostly due to elliptic flow fluctuations. However, the standard model of eccentricity fluctuations is unable to explain the large magnitude of v 4 / ( v 2 ) 2 in central collisions.

A generalization of the Boltzmann master equation theory in order to evaluate the angular distributions of the ejectiles emitted during the nucleon-nucleon interaction cascade which brings about the thermalization of the composite nucleus formed in the fusion of two heavy ions is discussed. The spectra of light ejectiles, up to α-particles, produced in many projectile-target combinations and at many different relative energies of the two ions are very reasonably reproduced.

We consider a model of thermalisation of pions due to elastic scattering and define the region of applicability of this model. In this region the chemical potential is positive. We analyse the absorptive and dispersive properties of pions during thermalisation, by calculating the pion collective potential. The pion gas can be thermally equilibrated but it will be out of chemical 3quilibrium. We define the degree of thermalisation near freeze-out at the level ∼ 70% for S + S and ∼ 90% for O + Au collisions at CERN. We find that the effect of the chemical potential in pion spectra is stronger than the temperature effect at p ⊥ ⩽ 200 MeV.

Simulation of heavy-ion (HI) collisions is performed within the quantum molecular dynamics (QMD) approach to investigate the thermalization process in 40 Ca+ 40 Ca collisions at energies up to 400 MeV/u. The results of the QMD simulation are analyzed within a hot Thomas-Fermi model to study the entropy evolution during these collisions. An anomalous decrease of the total one-body entropy at the decompression phase is found, which might be connected to a dynamical instability in the decompressed HI system. Here the many-body correlations are expected to be strong, leading to a break-down of the Fermi-gas-model description of the thermalization process.

This Session was meant to confront some of the ambitions and perplexities common to Low and High Energy Heavy Ion physicists (Section 1). Thermalisation was introduced (Section 2) and debated (Section 3) as a test case . An Outlook is ventured (Section 4) 1

Kinetic processes in pre-equilibrium parton matter are considered. We investigate chemical quark equilibration and parton thermalization, and their influence on electromagnetic and charmed probes.

Within the framework of stochastic transport equations in phase space, we study the dynamics of fluctuations on collective variables in homogeneous fermion systems. The transport coefficients are formally deduced in the relaxation-time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations: respectively, the BUU/Landau-Vlasov equation for the average phase-space trajectories and the equations for the averages and dispersions of the observables. Independently, we derive the general covariance matrix of phase-space fluctuations and then by projection, the dispersion on collective variables at equilibrium. Detailed numerical applications of the formalism are given; they show that the dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy, whatever is its degree of thermalization.

By simulating numerically the reaction dynamics of intermediate-energy heavy-ion collisions within the Boltzmann-Uehling-Uhlenbeck (BUU) transport model, we study systematically the onset of dynamical instabilities and nuclear multifragmentation in central collisions of 96 Mo + 96 Mo at beam energies of 55 and 100 MeV/nucleon. It is found that dynamical instabilities characterized by an imaginary adiabatic sound velocity in the central region of the reaction develop during the expansion phase of the reaction. Thermalization can be reached at about the same time when the dynamical instabilities set in. Multifragmentation patterns, geometries of final-fragment distributions as well as their dependence on the nuclear equation of state and the beam energy are also studied by making scatter plots of the one-body density distributions.

The hot Thomas-Fermi formalism, generalized for the case of two interpenetrating pieces of nuclear matter, is applied to investigate thermal properties (the local temperature and entropy) of the nonequilibrium nuclear matter formed during the time evolution of heavy-ion collisions at intermediate energies. Simulations of 20 Ne+ 20 Ne, 40 Ca+ 40 Ca and 93 Nb+ 93 Nb collisions at E lab = 100−400 MeV/u are performed within the framework of the quantum molecular dynamics approach. The sensitivity of thermal properties to the nuclear equation of state as well as their connection with some other dynamic observables are discussed. The anisotropic effects of the nonequilibrium phase space distribution on the thermalization process and the energy- and impact-parameter-dependence of the calculated thermal quantities during the reaction time are studied in detail.

The thermalisation process in heavy ion collisions is investigated employing the Quantum Molecular Dynamics approach. The validity of thermodynamical quantities, e.g. density, temperature and pressure are discussed. The investigation of the local degree of equilibrium leads to a three component picture, where in addition to the projectile and target a “fireball” component is defined, which includes all those nucleons which have suffered at least one hard collision. Local equilibration is observed in all of those components at all times. The dynamical evolution of the reaction is dominated by the interaction of both the projectile and the target with this fireball component and not, as was assumed in the two fluid model, by the interaction of projectile and target with each other. The structure of the stress tensor can be cast in a Newtonian form only for low energies. Then the values of the shear viscosity are in agreement with those values used in present viscous hydrodynamical calculations.

The reactions 40 Ar + KCl at eight energies from 0.36 to 1.8 GeV/u, 4 He + KCl at 977 and 40 Ar + Balg and 40 Ar + Pb 3 O 4 at 772 GeV/u measured in a Streamer Chamber experiment have been analyzed to determine the stopping power of nuclei, the degree of isotropy and thermalization achieved in central collisions, to search for collective expansion effects and to obtain compressional energies of bulk nuclear matter. Observables used were pion and proton exclusive final state measurements, ratios of total transverse to longitudinal momentum per event, momentum flux and Λ production. From the systematic discrepancy of the π − multiplicities produced in central collisions with respect to an intranuclear cascade model, compressional energies are extracted which fit a parabolic form of the nuclear matter equation of state with a compressibility constant of K = 240 MeV.