V. V. Begun

Power law in a microcanonical ensemble with scaling volume fluctuations

Volume fluctuations are introduced in a statistical modeling of relativistic particle collisions. The microcanonical ensemble is used, and the volume fluctuations are assumed to have specific scaling properties. This leads to the KNO scaling of the particle multiplicity distributions as measured in p + p interactions. A striking prediction of the model is a power law form of the single particle momentum spectrum at high momenta. Moreover, the mean multiplicity of heavy particles also decreases as a function of the particle mass according to a power law. Finally, it is shown that the dependence of the momentum spectrum on the particle mass and momentum reduces to the dependence on the particle energy. These results resemble the properties of particle production in collisions of high energy particles.

Multiplicity fluctuations in hadron-resonance gas

The charged hadron multiplicity fluctuations are considered in the canonical ensemble. The microscopic correlator method is extended to include three conserved charges: baryon number, electric charge, and strangeness. The analytical formulas are presented that allow us to include resonance decay contributions to correlations and fluctuations. We make the predictions for the scaled variances of negative, positive, and all charged hadrons in the most central Pb+Pb (Au+Au) collisions for different collision energies from SIS and AGS to SPS and RHIC.

Multiplicity fluctuations in relativistic nuclear collisions : statistical model versus experimental data

Multiplicity distributions of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the large volume limit. In the canonical ensemble conservation of three charges (baryon number, electric charge and strangeness) is enforced. In addition, in the micro-canonical ensemble, energy conservation is included. An analytical method is used to account for resonance decays. Multiplicity distributions and scaled variances for negatively charged hadrons are presented along the chemical freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC energies. Predictions obtained within different statistical ensembles are compared with preliminary NA49 experimental results on central Pb+Pb collisions in the SPS energy range. The measured fluctuations are significantly narrower than a Poisson reference distribution, and clearly favor expectations for the micro-canonical ensemble.

Quantum gases in the grand microcanonical ensemble near the thermodynamic limit

A new method is proposed for a treatment of ideal quantum gases in the grand microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number fluctuations in the system with exactly fixed total energy. It also gives the finite-volume corrections for the total average number of particles and for higher moments of the particle number distribution in a grand microcanonical system approaching the thermodynamic limit. The present consideration confirms our previous findings that the scaled variance for particle number fluctuations in the grand microcanonical ensemble is different from that in the grand canonical ensemble even in the thermodynamic limit.

Multiplicity distributions in canonical and microcanonical statistical ensembles

The aim of this paper is to introduce a new technique for the calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. A Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplace’s asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. A Gram–Charlier expansion additionally allows for the calculation of finite volume corrections. Analytical formulas are presented for the inclusion of resonance decay and finite acceptance effects directly into the partition function of the system. This paper consolidates and extends previously published results of the current investigation into the properties of statistical ensembles.

Strongly intensive measures for multiplicity fluctuations

The two recently proposed families of strongly intensive measures of fluctuations and correlations are studied within the hadron-string-dynamics (HSD) transport approach to nucleus–nucleus collisions. We consider the measures ΔKπ and ΣKπ for kaon and pion multiplicities in Au+Au collisions in a wide range of collision energies and centralities. These strongly intensive measures appear to cancel the participant number fluctuations. This allows to enlarge the centrality window in the analysis of event-by-event fluctuations for up to at least 10% of the most central collisions. We also present a comparison of the HSD results with the data of the NA49 and STAR Collaborations. HSD describes ΣKπ reasonably well. However, the HSD results depend monotonously on collision energy and do not reproduce the bump-dip structure of ΔKπ observed from the NA49 data in the region of the center of mass energy of the nucleon pair GeV. This observation deserves further study. The origin of this ‘structure’ is not connected with simple geometrical or limited acceptance effects, as these effects are taken into account in HSD simulations.

Crossover to Cluster Plasma in the Gas of Quark-Gluon Bags

We study a smooth crossover transition in the gas of quark–gluon bags. The equation of state at high temperature is that of the quark–gluon plasma. However, the system consists of the bags with finite volumes which are defined by the model parameters of the mass–volume bag spectrum. Possible structures in this cluster quark–gluon plasma are classified.

Non-perturbative effects for the Quark-Gluon Plasma equation of state

The non-perturbative effects for the Quark-Gluon Plasma (QGP) equation of state (EoS) are considered. The modifications of the bag model EoS are constructed to satisfy the main qualitative features observed for the QGP EoS in the lattice QCD calculations. A quantitative comparison with the lattice results is done for the SU(3) gluon plasma and for the QGP with dynamical quarks. Our analysis advocates a negative value of the bag constant B.

Pion number fluctuations and correlations in a statistical system with fixed isospin

The statistical system of pions with zero total isospin is studied. The suppression effects for the average yields due to isospin conservation are the same for

Fluctuations and correlations in pion system with fixed isospin

{\ensuremath{\pi}}^{0}