The phase diagram of hadronic matter

We interpret the phase structure of hadronic matter in terms of the basic dynamical and geometrical features of hadrons. Increasing the density of constituents of finite spatial extension, by increasing the temperature T or the baryochemical potential μ, eventually “fills the box” and eliminates the physical vacuum. We determine the corresponding transition as a function of T and μ through percolation theory. At low baryon density, this means a fusion of overlapping mesonic bags to one large bag, while at high baryon density, hard-core repulsion restricts the spatial mobility of baryons. As a consequence, there are two distinct limiting regimes for hadronic matter. We compare our results to those from effective chiral model studies.     

Hadrons in dense and hot matter

Theoretical issues and perspectives of hadronic matter at high baryon density are discussed with focus on the restoration of chiral symmetry and observable consequences.Received: 30 September 2002, Published online: 22 October 2003PACS: 25.75.-q Relativistic heavy-ion collisions - 21.65. + f Nuclear matter     

On the possibility of thermalization of heavy mesons in ultrarelativistic nuclear collisions

The phenomenological analysis and interpretation of experimental data from RHIC and LHC on the production of J/ψ and D mesons in heavy-ion collisions are performed within the two-component HYDJET++ model including the thermal and hard mechanisms of hadron production. It is shown that the thermal freeze-out of charmed mesons at RHIC energies occurs earlier than the thermal freeze-out of light hadrons (assumingly, simultaneously with chemical freeze-out), which indicates that J/ψ and D mesons are not in kinetic equilibrium with the formed hadronic matter. At the same time, a significant part of D mesons at LHC energies are in kinetic equilibrium with the formed thermalized matter, but J/ψ mesons are still characterized by early freeze-out.     

The hydrodynamics of hadron matter under a pion interferometric microscope

A method which makes it possible to examine the hydrodynamic motion of hadron matter is proposed. It is based on analysing bose-Einstein pion correlations. It enables the time, expansion rate and freeze-out temperature of the matter produced in the central region of high-energy hadronic and nuclear collisions to be measured.     

Space-time evolution of bulk QCD matter at RHIC

We introduce a combined fully three-dimensional macroscopic/microscopic transport approach employing relativistic 3D-hydrodynamics for the early, dense, deconfined stage of the reaction and a microscopic non-equilibrium model for the later hadronic stage where the equilibrium assumptions are not valid anymore. Within this approach we study the dynamics of hot, bulk QCD matter, which is being created in ultra-relativistic heavy-ion collisions at RHIC. In particular, we perform a detailed analysis of the reaction dynamics, hadronic freeze-out, transverse flow and elliptic flow. PACS 25.75.-q; 24.10.Nz; 24.10.Lx     

Thermal dileptons from quark and hadron phases of an expanding fireball

A fireball model with time evolution based on transport calculations is used to examine the dilepton emission rate of an ultra-relativistic heavy-ion collision. A transition from hadronic matter to a quark-gluon plasma at a critical temperature T _C between 130-170 MeV is assumed. We also consider a possible mixed phase scenario. We include thermal corrections to the hadronic spectra below T _C and use perturbation theory above T _C. The sensitivity of the spectra with respect to the freeze-out temperature, the initial fireball temperature and the critical temperature is investigated. Received: 4 August 2000 / Accepted: 14 November 2000     

Low mass dimuons produced in relativistic nuclear collisions

The NA60 experiment has measured low mass muon pair production in In-In collisions at 158A GeV with unprecedented precision. We show that these data are reproduced very well by a dynamical model with parameters scaled from fits to measurements of hadronic transverse mass spectra and Hanbury Brown-Twiss correlations in Pb-Pb and Pb-Au collisions at the same energy. The data are consistent with in-medium properties of rho and omega mesons at finite temperature and density as deduced from empirical forward-scattering amplitudes. Inclusion of the vacuum decay of the rho meson after freeze-out is necessary for an understanding of the mass and transverse momentum spectrum of dimuons with M less similar 0.9 GeV/c(2).     

Estimation of transport coefficients of dense hadronic and quark matter

In this study, we calculated transport coefficients including the shear viscosity and electrical conductivity relative to the density of dense hadronic and quark matter. By considering the simple massless limit for the quark matter and two different effective models for the hadronic matter, we estimated the transport coefficients of the two phases separately. Accordingly, density profiles of the transport coefficients were depicted in two parts: the phase-space part and the relaxation time part. From calculating the shear viscosity to density ratio, we also explored the nearly perfect fluid domain of the quark and hadronic matter.     

Equation of state of hadron resonance gas and the phase diagram of strongly interacting matter

The equation of state of hadron resonance gas at finite temperature and baryon density is calculated taking into account finite-size effects within the excluded-volume model. Contributions of known hadrons with masses up to 2 GeV are included in the zero-width approximation. Special attention is paid to the role of strange hadrons in the system with zero total strangeness. A density-dependent mean field is added to guarantee that the nuclear matter has a saturation point and a liquid-gas phase transition. The deconfined phase is described by the bag model with lowest order perturbative corrections. The phasetransition boundaries are found by using the Gibbs conditions with the strangeness neutrality constraint. The sensitivity of the phase diagram to the hadronic excluded volume and to the parametrization of the mean-field is investigated. The possibility of strangeness-antistrangeness separation in the mixed phase is analyzed. It is demonstrated that the peaks in the K/π and Λ/π excitation functions observed at low SPS energies can be explained by a nonmonotonous behavior of the strangeness fugacity along the chemical freeze-out line. The text was submitted by the authors in English.     

MULTI-LAMBDA MATTER IN A CHIRAL HADRONIC MODEL

Multi-lambda matter is investigated in the framework of a chiral hadronic model. It is shown that multi-lambda matter consisting of {N,Λ} is a metastable state as the strangeness per baryon and the density of hadronic matter are varied. The effective lambda mass decreases as the baryon density increases, and remains larger than that of the nucleon.     

Excitation energy as a basic variable to control nuclear disassembly

Thermodynamical features of Xe system is investigated as functions of temperature and freeze-out density in the frame of lattice gas model. The calculation shows different temperature dependence of physical observables at different freeze-out density. In this case, the critical temperature when the phase transition takes place depends on the freeze-out density. However, a unique critical excitation energy %and the same excitation reveals regardless of freeze-out density when the excitation energy is used as a variable instead of temperature. Moreover, the different behavior of other physical observables with temperature due to different ρ_f vanishes when excitation energy replaces temperature. It indicates that the excitation energy can be seen as a more basic quantity to control nuclear disassembly. Received: 25 November 1998 /Revised version: 20 January 1999     

Initial temperature and EoS of quark matter via direct photons

The time evolution of the quark gluon plasma created in gold-gold collisions of the Relativistic Heavy Ion Collider (RHIC) can be described by hydro-dynamical models. Distribution of hadrons reflects the freeze-out state of the matter. To investigate the time evolution one needs to analyze penetrating probes, such as direct photon spectra. Distributions of low energy photons was published in 2010 by PHENIX. In this paper we analyze a 3 + 1 dimensional solution of relativistic hydrodynamics and calculate momentum distribution of direct photons. Using earlier fits of this model to hadronic spectra, we compare photon calculations to measurements and find that the initial temperature of the center of the fireball is at least 519 ± 12 MeV, while for the equation of state we get c _s = 0.36 ± 0.02.     

The Hagedorn temperature and partition thermodynamics

We review the resonance gas formalism of hadron thermodynamics and recall that an exponential increase of the resonance spectrum leads to a limiting temperature of hadronic matter. We then show that the number p(n) of ordered partitions of an integer n grows exponentially with n and satisfies the integer counterpart of the statistical bootstrap equation. Considering the set of all partitions as a Gibbs ensemble provides a partition thermodynamics which is also governed by a limiting temperature, determined by the combinatorial structure of the problem. Further associating intrinsic quantum numbers to integers results in a phase diagram equivalent to that found in QCD for hadronic matter as a function of temperature and baryochemical potential.Received: 16 January 2004, Published online: 19 March 2004Dedicated to Rolf Hagedorn, 1919-2003.     

Examining the crossover from the hadronic to partonic phase in QCD

A mechanism, consistent with color confinement, for the transition between perturbative and physical vacua during the gradual crossover from the hadronic to partonic phase is proposed. The essence of this mechanism is the appearance and growing up of a kind of grape-shape perturbative vacuum inside the physical one. A percolation model based on simple dynamics for parton delocalization is constructed to exhibit this mechanism. The crossover from hadronic matter to sQGP (strongly coupled quark-gluon plasma) as well as the transition from sQGP to weakly coupled quark-gluon plasma with increasing temperature is successfully described by using this model.     

Deconfinement transition: a three dimensional model

We present a three–dimensional model for quark matter with a density dependent quark–quark (confining) potential, which allows to describe a sort of deconfinement transition as the system evolves from a low density assembly of bound structures to a high density free Fermi gas of quarks. We consider different confining potentials, some of which successfully utilized in hadron spectroscopy. We find that a proper treatment of the many–body correlations induced by the medium is essential to disentangle the different nature of the two (hadronic and deconfined) phases of the system. For this purpose the ground state energy per particle and the pair correlation function are investigated. Received: 10 June 1998 / Revised version: 24 September 1998     

Partonic effects on pion interferometry at the relativistic heavy-ion collider

Using a multiphase transport model that includes both initial partonic and final hadronic interactions, we study the pion interferometry at the Relativistic Heavy-Ion Collider. We find that the two-pion correlation function is sensitive to the magnitude of the parton-scattering cross section, which controls the parton density at which the transition from the partonic to hadronic matter occurs. Also, the emission source of pions is non-Gaussian, leading to source radii that can be more than twice larger than the radius parameters extracted from a Gaussian fit to the correlation function.     

Electroosmotic Flow, Ionic Currents, and Pressure-Induced Flow in Microsystem Channel Networks: NMR Mapping and Computational Fluid Dynamics Simulations

Using nuclear magnetic resonance (NMR) velocity mapping and NMR current density mapping as well as finite-element computational fluid dynamics methods, transport in microsystem electrolytic cells with increasing complexity has been examined ranging from single straight channels to random-site percolation clusters. This sort of system is considered as paradigm for more or less complex devices in microsystem technology. Corresponding model objects were designed on a computer and milled into ceramic (polar) or polystyrene (nonpolar) matrices. The pore space was filled with electrolyte solutions. Maps of the following quantities were recorded: velocity of hydrodynamic flow driven by external pressure gradients, velocity of electroosmotic flow (EOF), ionic current density in the presence of EOF, ionic current density in the absence of EOF. As far as possible, the experiments were supplemented by computational fluid dynamics simulations. It is shown that EOF, as well as the electric current, leads to recirculation patterns in closed complex structures such as percolation clusters. Remarkably, all transport patterns turned out to be dissimilar, and the occurrence and positions of eddies do not coincide in the different maps. Velocity histograms and the mean velocity as a function of the porosity have been evaluated. An EOF percolation transition is found at the geometrical percolation threshold. The combined application of NMR techniques for the quantitative, noninvasive visualization of the total variety of hydroand electrodynamics in the same channel system promises to become a powerful tool for design purposes in microsystem technology. Authors' address: Rainer Kimmich, Sektion Kernresonanzspektroskopie, Universit?t Ulm, Albert-Einstein-Alee 11, 89069 Ulm, Germany