Quasi-particle model of QGP - a revisit

The quasi-particle model of quark gluon plasma (QGP) is revisited here with thermodynamically consistent formalism, 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 one system dependent parameter 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 $\epsilon$ first from grand partition function of quasi-particle QGP and then derive all other thermodynamic functions from $\epsilon$. Quasi-particles are assumed to have temperature dependent mass equal to plasma frequency. Energy density, pressure and speed of sound 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.Comment: 7 pages (LaTex), 6 figures, revised with correction and new result

Self-consistent quasi-particle model for relativistic 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.Comment: 9 pages, 2 figure

Comments on "Stronger Uncertainty Relations for All Incompatible Observables"

Recently, Maccone and Pati \cite{pa.1} derived new uncertainty relations which they claim to be stronger than Heisenberg-Robertson or Schrodinger uncertainty relations. Here we comment that their work is a special case of a more general uncertainty relation and we reexamine some of their conclusions.Comment: 2 pages, comments on paper appeared in Phys. Rev. Lett. recentl

Is QGP really a liquid ?

Here we address the question regarding the nature of quark gluon plasma (QGP), whether it is a liquid or strongly coupled plasma (SCP), using two different phenomenological models, namely quasi-particle model (qQGP) and strongly coupled quark gluon plasma (SCQGP). First we compare these two models, both of which explains the results of lattice simulation of quantum chromodynamics, as a function of plasma parameter and conclude that the QGP is largely ($T > 1.5 T_c$) SCQGP and only for $T < 1.5 T_c$ it may be a liquid.Comment: 9 pages, 3 figures, article (Revised based on comments

Generalized Cauchy-Schwarz inequality and Uncertainty Relation

A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.Comment: 7 pages, articl

General and Stronger Uncertainty Relation

Recently, Maccone and Pati [Phys. Rev. Lett. {\bf 113}, 260401 (2014)] derived few inequalities among variances of incompatible operators which they called stronger uncertainty relations, stronger than Heisenberg-Robertson or Schrodinger uncertainty relations. Here we generalize their study to get infinite number of such inequalities and propose that only one of them may be the correct uncertainty relation between incompatible operators. We get back well known uncertainty relations of Heisenberg-Robertson and Schrodinger under certain limits. We also reexamine the conclusions of Maccone and Pati and comment on their work.Comment: 6 pages, articl

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, $\beta_k$, unlike Mayer's work where it depends on reducible cluster integral, $b_l$. The virial expansion, criteria for it's validity and criteria for condensation, etc. are derived from our generating function. All earlier Mayer's results are obtained from this new generating function.Comment: article, 9 pages, revise

Thermodynamic Behaviour of Magnetized QGP within the Self-Consistent Quasiparticle Model

The self-consistent quasiparticle model has been successful in studying QCD thermodynamics. In this model, the medium effects are taken into account by considering quarks and gluons as quasiparticles with temperature-dependent masses which are proportional to the plasma frequency. The present work involves the extension of this model in the presence of magnetic fields. We have included the effect of the magnetic field by considering relativistic Landau Levels. The quasiparticle masses are then found to be dependent on both temperature and magnetic field. The thermomagnetic mass thus defined allows obtaining the thermodynamics of magnetized quark matter within the self-consistent quasiparticle model. The model then has been applied to the case of 2-flavor Quark-Gluon Plasma and the equation of state obtained in the presence of magnetic fields

Generalized Darboux transformation and N-th order rogue wave solution of a general coupled nonlinear Schr\"{o}dinger equations

We construct a generalized Darboux transformation (GDT) of a general coupled nonlinear Schr\"{o}dinger (GCNLS) system. Using GDT method we derive a recursive formula and present determinant representations for N-th order rogue wave solution of this system. Using these representations we derive first, second and third order rogue wave solutions with certain free parameters. By varying these free parameters we demonstrate the formation of triplet, triangle and hexagonal patterns of rogue waves.Comment: 27 pages, 7 figures and Accepted for Publication in Commun. Nonlinear Sci. Numer. Simu

On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schr\"odinger equations

We construct Darboux transformation of a coupled generalized nonlinear Schr\"odinger (CGNLS) equations and obtain exact analytic expressions of breather and rogue wave solutions. We also formulate the conditions for isolating these solutions. We show that the rogue wave solution can be found only when the four wave mixing parameter becomes real. We also investigate the modulation instability of the steady state solution of CGNLS system and demonstrate that it can occur only when the four wave mixing parameter becomes real. Our results give an evidence for the connection between the occurrence of rogue wave solution and the modulation instability.Comment: 14 pages, 3 figures, To appear in Wave Motio