Relativistic Kinetic Equations for Finite Domains and Freeze-out Problem

The relativistic kinetic equations for the two domains separated by the hypersurface with both space- and time-like parts are derived. The particle exchange between the domains separated by the time-like boundaries generates source terms and modifies the collision term of the kinetic equation. The correct hydrodynamic equations for the ``hydro+cascade'' models are obtained and their differences from existing freeze-out models of the hadronic matter are discussed

Particle Freeze-out and Discontinuities in Relativistic Hydrodynamics

Freeze-out of particles in relativistic hydrodynamics is considered across a 3-dimensional space-time hypersurface. The conservation laws for time-like parts of the freeze-out hypersurface require different values of temperature, baryonic chemical potential and flow velocity in the fluid and in the final particle spectra. We analyze this freeze-out discontinuity and its connection to the shock-wave phenomena in relativistic hydrodynamics.Comment: 6 figure

Exactly Solvable Model for the QCD Tricritcal Endpoint

An inclusion of temperature and chemical potential dependent surface tension into the gas of quark-gluon bags model resolves a long standing problem of a unified description of the first and second order phase transition with the cross-over. The suggested model has an exact analytical solution and allows one to rigorously study the vicinity of the critical endpoint of the deconfinement phase transition. It is found that at the curve of a zero surface tension coefficient there must exist the surface induced phase tranition of the 2-nd or higher order. The present model predicts that the critical endpoint (CEP) of quantum chromodynamics is the tricritical endpoint.Comment: 14 pages, 3 figures, invited talk given at the International Workshop ``Relativistic Nuclear Physics: from Nuclotron to LHC Energies'', Kiev, Ukraine, June 18-22, 200

Surface Partition of Large Fragments

The surface partition of large fragments is derived analytically within a simple statistical model by the Laplace-Fourier transformation method. In the limit of small amplitude deformations, a suggested Hills and Dales Model reproduces the leading term of the famous Fisher result for the surface entropy with an accuracy of a few percent. The surface partition of finite fragments is discussed as well.Comment: 4 pages, 1 figur

Exactly Solvable Models: The Road Towards a Rigorous Treatment of Phase Transitions in Finite Systems

We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical multifragmentation model, the Gas of Bags Model and the Hills and Dales Model of surface partition. Thus, the Laplace-Fourier transform allows one to study the nuclear matter equation of state, the equation of state of hadronic and quark gluon matter and surface partitions on the same footing. A complete analysis of the isobaric partition singularities of these models is done for finite systems. The developed formalism allows us, for the first time, to exactly define the finite volume analogs of gaseous, liquid and mixed phases of these models from the first principles of statistical mechanics and demonstrate the pitfalls of earlier works. The found solutions may be used for building up a new theoretical apparatus to rigorously study phase transitions in finite systems. The strategic directions of future research opened by these exact results are also discussed.Comment: Contribution to the ``World Consensus Initiative III, Texas A & M University, College Station, Texas, USA, February 11-17, 2005, 21

Modified Boltzmann Transport Equation and Freeze Out

We study Freeze Out process in high energy heavy ion reaction. The description of the process is based on the Boltzmann Transport Equation (BTE). We point out the basic limitations of the BTE approach and introduce Modified BTE. The Freeze Out dynamics is presented in the 4-dimensional space-time in a layer of finite thickness, and we employ Modified BTE for the realistic Freeze Out description.Comment: 9 pages, 2 figure

The complement: a solution to liquid drop finite size effects in phase transitions

The effects of the finite size of a liquid drop undergoing a phase transition are described in terms of the complement, the largest (but still mesoscopic) drop representing the liquid in equilibrium with the vapor. Vapor cluster concentrations, pressure and density from fixed mean density lattice gas (Ising) model calculations are explained in terms of the complement. Accounting for this finite size effect is key to determining the infinite nuclear matter phase diagram from experimental data.Comment: Four two column pages, four figures, two tables; accepted for publication in PR