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

Charmonium Production from the Secondary Collisions at LHC Energy

We consider the charmonium production in thermalized hadronic medium created in ultrarelativistic heavy ion collisions at LHC energy. The calculations for the secondary $J/\psi$ and $\psi^,$ production by $D\bar D$ annihilation are performed within a kinetic model taking into account the space-time evolution of a longitudinally and transversely expanding medium. We show that the secondary charmonium production appears almost entirely during the mixed phase and it is very sensitive to the charmonium dissociation cross section with co-moving hadrons. Within the most likely scenario for the dissociation cross section of the $J/\psi$ mesons their regeneration in the hadronic medium will be negligible. The secondary production of $\psi^,$ mesons however, due to their large cross section above the threshold, can substantially exceed the primary yield.Comment: ps file 11

Topological calculation of the phase of the determinant of a non self-adjoint elliptic operator

We study the zeta-regularized determinant of a non self-adjoint elliptic operator on a closed odd-dimensional manifold. We show that, if the spectrum of the operator is symmetric with respect to the imaginary axis, then the determinant is real and its sign is determined by the parity of the number of the eigenvalues of the operator, which lie on the positive part of the imaginary axis. It follows that, for many geometrically defined operators, the phase of the determinant is a topological invariant. In numerous examples, coming from geometry and physics, we calculate the phase of the determinants in purely topological terms. Some of those examples were known in physical literature, but no mathematically rigorous proofs and no general theory were available until now.Comment: To appear in Communications of Mathematical Physic

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

Viscosities in the Gluon-Plasma within a Quasiparticle Model

A phenomenological quasiparticle model, featuring dynamically generated self-energies of excitation modes, successfully describes lattice QCD results relevant for the QCD equation of state and related quantities both at zero and non-zero net baryon density. Here, this model is extended to study bulk and shear viscosities of the gluon-plasma within an effective kinetic theory approach. In this way, the compatibility of the employed quasiparticle ansatz with the apparent low viscosities of the strongly coupled deconfined gluonic medium is shown.Comment: 4 pages, 1 figure. To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee, US

Kurtosis and compressibility near the chiral phase transition

The properties of net quark number fluctuations in the vicinity of the QCD chiral phase transition are discussed in terms of an effective chiral model in the mean-field approximation. We focus on the ratio of the fourth- to second- order cumulants (kurtosis) and the compressibility of the system and discuss their dependence on the pion mass. It is shown that near the chiral phase transition, both observables are sensitive to the value of $m_\pi$. For physical $m_\pi$, the kurtosis exhibits a peak whereas the inverse compressibility shows a dip at the pseudocritical temperature. These structures disappear for large $m_\pi$. Our results, obtained in an effective model with two flavors, are qualitatively consistent with recent results of 2+1 flavor lattice gauge theory. We also discuss the high- and low-temperature properties of these observables and the role of the coupling of the quark degrees of freedom to the Polyakov loop