From chemical freezeout to critical conditions in heavy ion collisions

We compare the statistical thermodynamics of hadron resonance gas with recent LGT results at finite chemical potential. We argue that for $T\leq T_c$ the equation of state derived from Monte--Carlo simulations of two quark--flavor QCD at finite chemical potential is consistent with that of a hadron resonance gas when applying the same set of approximations as used in LGT calculations. We indicate the relation of chemical freezeout conditions obtained from a detailed analysis of particle production in heavy ion collisions with the critical conditions required for deconfinement. We argue that the position of a hadron--quark gluon boundary line in temperature chemical potential plane can be determined in terms of the resonance gas model by the condition of fixed energy density.Comment: Talk given at BUDAPEST'2004 Workshop on 'Hot and Dense Matter in Relativistic Heavy Ion Physics', Budapest, March 24-27, 200

The Statistical Model of Hadrogenesis in A--A collisions from AGS to SPS and RHIC

We discuss experimental data on particle yields and particle spectra obtained in heavy ion collisions in a very broad energy range from SIS/GSI through AGS/BNL up to SPS/CERN and RHIC/BNL. We argue that in this broad energy range hadronic yields and their ratios resemble a thermal equilibrium population along a unified freeze--out curve determined by the condition of fixed energy/particle = 1 GeV. At RHIC and top SPS, thermal parameters are consistent within error with the critical conditions required for deconfinement. This, together with the particular distribution of strangeness within a collision fireball, could indicate that chemical equilibrium is a direct consequence of parton to hadron transition, which populates a state of maximum entropy. At lower energies equilibration in A--A collisions should appear through hadronic interactions and rescatterings.Comment: Plenary talk given at: International Nuclear Physics Conference, INPC2001, Berkeley, USA, August 200

Unbalanced Allocations

We consider the unbalanced allocation of $m$ balls into $n$ bins by a randomized algorithm using the "power of two choices". For each ball, we select a set of bins at random, then place the ball in the fullest bin within the set. Applications of this generic algorithm range from cost minimization to condensed matter physics. In this paper, we analyze the distribution of the bin loads produced by this algorithm, considering, for example, largest and smallest loads, loads of subsets of the bins, and the likelihood of bins having equal loads

Thermodynamics of Van der Waals Fluids with quantum statistics

We consider thermodynamics of the van der Waals fluid of quantum systems. We derive general relations of thermodynamic functions and parameters of any ideal gas and the corresponding van der Waals fluid. This provides unambiguous generalization of the classical van der Waals theory to quantum statistical systems. As an example, we apply the van der Waals fluid with fermi statistics to characterize the liquid-gas critical point in nuclear matter. We also introduce the Bose-Einstein condensation in the relativistic van der Waals boson gas, and argue, that it exhibits two-phase structure separated in space

Strangeness enhancement and Energy dependence in Heavy Ion Collisions

The canonical statistical model analysis of strange and multistrange hadron production in central A-A relative to p-p/p-A collisions is presented over the energy range from $\sqrt s=8.73$ GeV up to $\sqrt s =130$ GeV. It is shown that the relative enhancement of strange particle yields from p-p/p-A to A-A collisions substantially increases with decreasing collision energy. It is largest at $\sqrt s= 8.7$ GeV, where the enhancement of $\Omega,\Xi$ and $\Lambda$ is of the order of 100, 20 and 3, respectively. In terms of the model these results are due to the canonical suppression of particle thermal phase space at lower energies, which increases with the strangeness content of the particle and with decreasing size of the collision fireball. The comparison of the model with existing data on energy dependence of the kaon/pion ratio is also discussed

Thermodynamics of the low density excluded volume hadron gas

We consider thermodynamics of the excluded volume particles at finite temperature and chemical potential, in the low density approximation. We assume Boltzmann statistics and study the influence of the excluded volume on an ideal gas thermodynamics at the same temperature, pressure and numbers of particles. We show, that considering the change of the free enthalpy due to the excluded volume, and using the Maxwell identities, one can derive relevant thermodynamic functions and parameters of multi-component gases. The derivation is quite general as particles may have different sizes and shapes which can also depend on their momenta. Besides it's simplicity and generality, our approach has the advantage of eliminating the transcendental equations occurring in earlier studies. A representative example of the excluded volume thermodynamics is the single-component gas of hard spheres. For this case, using the viral expansion, the validity limits of the low-density approximation are also discussed.Comment: 7 pages, 4 figur