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

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

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

Momentum scale dependence of the net quark number fluctuations near chiral crossover

We investigate properties of the net baryon number fluctuations near chiral crossover in a hot and dense medium of strongly interacting quarks. The chirally invariant quark-antiquark interactions are modeled by an effective quark-meson Lagrangian. To preserve remnants of criticality in the O(4) universality class, we apply the functional renormalization group method to describe thermodynamics near chiral crossover. Our studies are focused on the influence of the momentum cuts on the critical behavior of different cumulants of the net quark number fluctuations. We use the momentum scale dependence of the flow equation to examine how the suppression of the momentum modes in the infrared and ultraviolet regime modifies generic properties of fluctuations expected in the O(4) universality class. We show, that the pion mass $m_\pi$ is a natural soft momentum scale at which cumulants are saturated at their critical values, whereas for scales larger than $2m_\pi$ the characteristic O(4) structure of the higher order cumulants get lost. These results indicate, that when measuring fluctuations of the net baryon number in heavy ion collisions to search for a partial restoration of chiral symmetry or critical point, a special care have to be made when introducing kinematical cuts on the fluctuation measurements.Comment: 15 pages, 8 figures. To appear in Prog. Theor. Exp. Phy

Weak and strong coupling limits of the Boltzmann equation in the relaxation-time approximation

We consider a momentum dependent relaxation time for the Boltzmann equation in the relaxation time approximation. We employ a power law parametrization for the momentum dependence of the relaxation time, and calculate the shear and bulk viscosity, as well as, the charge and heat conductivity. We show, that for the two popular parametrizations, referred to as the linear and quadratic ansatz, one can obtain transport coefficients which corresponds to the weak and strong coupling regimes, respectively. We also show that, for a system of massless particles with vanishing chemical potential, the off-equilibrium corrections to the phase-space distribution function calculated with the quadratic ansatz are identical with those of the Grad's 14-moment method.Comment: 6 page

Criticality of the net-baryon number probability distribution at finite density

We compute the probability distribution $P(N)$ of the net-baryon number at finite temperature and quark-chemical potential, $\mu$, at a physical value of the pion mass in the quark-meson model within the functional renormalization group scheme. For $\mu/T<1$, the model exhibits the chiral crossover transition which belongs to the universality class of the $O(4)$ spin system in three dimensions. We explore the influence of the chiral crossover transition on the properties of the net baryon number probability distribution, $P(N)$. By considering ratios of $P(N)$ to the Skellam function, with the same mean and variance, we unravel the characteristic features of the distribution that are related to $O(4)$ criticality at the chiral crossover transition. We explore the corresponding ratios for data obtained at RHIC by the STAR Collaboration and discuss their implications. We also examine $O(4)$ criticality in the context of binomial and negative-binomial distributions for the net proton number.Comment: 7 pages, 4 figures, to appear in Phys.Lett.

Relativistic second-order dissipative hydrodynamics at finite chemical potential

Starting from the Boltzmann equation in the relaxation time approximation and employing a Chapman-Enskog like expansion for the distribution function close to equilibrium, we derive second-order evolution equations for the shear stress tensor and the dissipative charge current for a system of massless quarks and gluons. The transport coefficients are obtained exactly using quantum statistics for the phase space distribution functions at non-zero chemical potential. We show that, within the relaxation time approximation, the second-order evolution equations for the shear stress tensor and the dissipative charge current can be decoupled. We find that, for large values of the ratio of chemical potential to temperature, the charge conductivity is small compared to the coefficient of shear viscosity. Moreover, we show that in the relaxation-time approximation, the limiting behaviour of the ratio of heat conductivity to shear viscosity is qualitatively similar to that obtained for a strongly coupled conformal plasma.Comment: v3: 6 pages, 2 figure, published versio

Probing QCD chiral cross over transition in heavy ion collisions with fluctuations

We argue that by measuring higher moments of the net proton number fluctuations in heavy ion collisions (HIC) one can probe the QCD chiral cross over transition experimentally. We discuss the properties of fluctuations of the net baryon number in the vicinity of the chiral crossover transition within the Polyakov loop extended quark-meson model at finite temperature and baryon density. The calculation includes non-perturbative dynamics implemented within the functional renormalization group approach. We find a clear signal for the chiral crossover transition in the fluctuations of the net baryon number. We address our theoretical findings to experimental data of STAR Collaboration on energy and centrality dependence of the net proton number fluctuations and their probability distributions in HIC