Vishnu M. Bannur

Comments on quasiparticle models of quark-gluon plasma

Abstract Here we comment on the thermodynamic inconsistency problem and the reformulation of statistical mechanics of widely studied quasiparticle models of quark–gluon plasma. Their starting relation, the expression for pressure itself is a wrong choice and lead to thermodynamic inconsistency and the requirements of the reformulation of statistical mechanics. We propose a new approach to the problem using the standard statistical mechanics and is thermodynamically consistent. We also show that the other quasiparticle models may be obtained from our general formalism as a special case under certain restrictive condition. Further, as an example, we have applied our model to explain the nonideal behaviour of gluon plasma and obtained a remarkable good fit to the lattice results by adjusting just a single parameter.

Revisiting the quasi-particle model of the quark–gluon plasma

The quasi-particle model of quark gluon plasma (QGP) is revisited here with a new method, different from earlier studies, without the need of temperature dependent bag constant as well as other effects such as confinement effects, effective degrees of freedom etc. Our model has only two system dependent parameters and surpraisingly good fit to lattice results for gluon plasma, 2-flavor and 3-flavor QGP are obtained. The basic idea is to evaluate energy density ε first from grand partition function of quasi-particle QGP and then derive all other thermodynamic functions from ε. Quasi-particles are assumed to have temperature dependent mass equal to plasma frequency. Energy density, pressure and speed of sound at zero chemical potential are evaluated and compared with available lattice data. We further extend the model to finite chemical potential, without any new parameters, to obtain quark density, quark susceptibility etc. and fits very well with the lattice results on 2-flavor QGP. PACS Nos : 12.38.Mh, 12.38.Gc, 05.70.Ce, 52.25.Kn

Strongly coupled quark gluon plasma (SCQGP)

We propose that the reason for the non-ideal behaviour seen in lattice simulation of quark gluon plasma (QGP) and ultrarelativistic heavy ion collision experiments is that the QGP near Tc and above is a strongly coupled plasma (SCP), i.e., a strongly coupled quark gluon plasma (SCQGP). It is remarkable that the widely used equation of state of SCP in QED (quantum electrodynamics) very nicely fits lattice results on all QGP systems, with proper modifications to include colour degrees of freedom and the running coupling constant. Results on pressure in pure gauge, 2-flavours and 3-flavours QGP can all be explained by treating QGP as SCQGP, as demonstrated here. Energy density and speed of sound are also presented for all three systems. We further extend the model to systems with finite quark mass and reasonably good fits to lattice results are obtained for (2+1)-flavours and 4-flavours QGP. Hence it is a unified model, namely SCQGP, to explain the non-ideal QGP seen in lattice simulations with just two system dependent parameters.

Self-consistent quasiparticle model for quark-gluon plasma

Here we present a self-consistent quasiparticle model for quark-gluon plasma (QGP) and apply it to explain the nonideal behavior seen in lattice simulations. The basic idea, borrowed from electrodynamic plasma, is that the gluons acquire mass as they propagate through plasma due to collective effects and are approximately equal to the plasma frequency. The statistical mechanics and thermodynamics of such a system is studied by treating it as an ideal gas of massive gluons. Since mass or plasma frequency depend on density, which itself is a thermodynamic quantity, the whole problem needs to be solved self-consistently. This new quasiparticle model of QGP explains remarkably well the lattice simulation results of gluon plasma by adjusting just a single phenomenological parameter. Further, we extend our model to study gluon plasma using the exact, ultrarelativistic dispersion relation and again obtain a good fit to lattice results.

Self-consistent quasiparticle model for 2,3, and (2 + 1) flavor QGP

The quasiparticle model of quark gluon plasma is the statistical mechanics of noninteracting particles with medium dependent mass related to plasma frequency, which is proposed to describe the thermodynamics of the medium itself. At the relativistic limit, the plasma frequency depends on the number density and temperature. The number density is a thermodynamic quantity of the medium which in turn depends on plasma frequency. Hence, one needs to solve this problem self-consistently instead of using perturbative expressions for plasma frequency. Here we carry out such self-consistent calculations using our recently developed new formulations of the quasiparticle model. By adjusting a single parameter for each system, a remarkably good fit to results of lattice simulation of quantum chromodynamics is obtained for 2, 3, and (2+1) flavor quark gluon plasma systems, first, with zero chemical potential. Then, it is extended to systems with finite chemical potential and fits very well to the lattice results without any new parameter.

Equation of state for a non-ideal quark gluon plasma

Abstract We have derived the equation of state (EOS) for a quark-antiquark plasma in which the quarks and antiquarks are not free but interacting via “Coulomb + linear confinement” interaction, using Mayers classical cluster expansion method. This EOS, when used for the gluon plasma, fits the lattice results reasonably well.

Quasi-particle model for QGP with nonzero densities

We discuss a new quasi-particle model for quark gluon plasma (QGP) with nonzero densities and study the thermodynamics of (2+1)-flavor QGP. Our model with a minimum number of adjustable parameters explains remarkably well the lattice simulation results of Fodor et al. [1].We discuss a new single parameter quasi-particle model and study the thermodynamics of (2+1)-flavor quark gluon plasma (QGP). Our model with a single parameter explains remarkably well the lattice simulation results of Fodor et. al. Phys. Lett. B568, 73 (2003).

Virial expansion and condensation with a new generating function

Mayer’s convergence method for virial expansion and condensation is studied using a new generating function for canonical partition function, which directly depends on irreducible cluster integral, βk, unlike Mayer’s work where it depends on reducible cluster integral, bl. The virial expansion, criteria for its validity and criteria for condensation, etc. are derived from our generating function. All earlier Mayer’s results are obtained from this new generating function.

Self-consistent quasiparticle model results for ultrarelativistic electron-positron thermodynamic plasma

Relativistic plasma with radiation at thermodynamic equilibrium is ageneral system of interest in astrophysics and high energy physics. We develop a new self-consistent quasi-particle model for such a system to take account of collective behaviour of plasma andthermodynamic properties are derived. It is applied to electrodynamic plasma and quark gluon plasma and compared with existing results.

STATISTICAL MECHANICS OF CONFINED QUANTUM PARTICLES

We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which is applicable in quark gluon plasma (QGP), astrophysics, Bose–Einstein condensation (BEC) etc. Detailed study of QGP system is carried out and compared with lattice results. Furthermore, as an application, our equation of state (EoS) of QGP is used to study compact stars like quark star.