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Anisotropic systems of quarks and gluons, which at least for sufficiently short space-time intervals can be treated as homogeneous and static, are considered. The gluon polarization tensor of such a system is explicitly computed within the semiclassical kinetic and hard loop diagrammatic theories. The equivalence of the two approaches is demonstrated. The quark self-energy is computed as well, and finally, the dispersion relations of quarks and gluons in the anisotropic medium are discussed.

Employing a previously derived formulation, and extending the treatment from purely transverse modes to wave vectors having a longitudinal component, we discuss the prospects for the occurrence of Weibel-type color-current filamentation in high-energy nuclear collisions. Numerical solutions of the dispersion equation for a number of scenarios relevant to RHIC and LHC suggest that modes with (predominantly transverse) wave numbers of several hundred MeV may become moderately agitated during the early collision stage. The emergence of filamentation helps to speed up the equilibration of the parton plasma and it may lead to non-statistical azimuthal patterns in the hadron final state.Comment: 11 pages, RevTex, 13 (e)ps files (revised for PRC

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We derive hydrodynamic-like equations that are applicable to short-time scale color phenomena in the quark-gluon plasma. The equations are solved in the linear response approximation, and the gluon polarization tensor is derived. As an application, we study the collective modes in a two-stream system and find plasma instabilities when the fluid velocity is larger than the speed of sound in the plasma. The chromo-hydrodynamic approach, discussed here in detail, should be considered as simpler over other approaches and well-designed for numerical studies of the dynamics of an unstable quark-gluon plasma. I. INTRODUCTIONBulk features of electromagnetic plasmas are usually studied by means of fluid equations [1]. To get more detailed information, one refers to kinetic theory [1]. Since the fluid equations are noticeably simpler than the kinetic ones, the hydrodynamic approach is also frequently used in numerical simulations of the plasma evolution, studies of the nonlinear dynamics, etc. [1]. The situation in the field of quark-gluon plasma studies is rather different. Although chromo-hydrodynamics equations were discussed by several authors over a long period of time [2-12], they were not carefully studied. The field of their applicability was not established and very few important results were obtained by means of them. Consequently, the chromo-hydrodynamics has not attracted much attention. Instead, field theory diagrammatic methods have been successfully applied to reveal equilibrium properties of the quark-gluon plasma [13], while transport theory [14][15][16] proved efficient in the non-equilibrium studies. In particular, the important role of instabilities in the quark-gluon plasma evolution was clarified within the kinetic theory approach, see the review [17]. The kinetic equations were also a basis of extensive numerical simulations of the unstable QCD plasma [18][19][20][21][22][23][24]. The early stage of relativistic heavy-ion collisions, when the quark-gluon system is produced, was effectively studied using methods of classical field theory, see e.g. the review [25] and very recent publications [26,27].Inspired by the success of hydrodynamic methods in the electromagnetic plasma, we discuss the approach to be applied to the quark-gluon plasma. Before going to the main subject of our study, however, a very important point has to be clarified. Real hydrodynamics deals with systems which are in local equilibrium, and thus it is only applicable at sufficiently long time scales. The continuity and the Euler or Navier-Stokes equations are supplemented by the equation of state to form a complete set of equations. The equations can be derived from kinetic theory, using the distribution function of local equilibrium, which by definition maximizes the entropy density, and thus the function cancels the collision terms of the transport equations. Such a real chromo-hydrodynamics was derived in [10] where the state of local equilibrium was found, using the collision term of the Waldman-Snider form. The chromo-hydrod...

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Fluctuations of the chemical composition of the hadronic system produced in nuclear collisions are discussed using the Φ−measure which has been earlier applied to study the transverse momentum fluctuations. The measure is expressed through the moments of the multiplicity distribution and then the properties of Φ are discussed within a few models of multiparticle production. A special attention is paid to the fluctuations in the equilibrium ideal quantum gas. The system of kaons and pions, which is particularly interesting from the experimental point of view, is discussed in detail. PACS: 25.75.+r, 24.60.Ky,24.60.-k Keywords: Relativistic heavy-ion collisions; Fluctuations; Thermal model There are many sorts of hadrons produced in high energy collisions. The ratios of multiplicities of particles of given species to the total particle number characterize the chemical composition of the collision final state. The composition is expected to reflect the collisions dynamics. Generation of the quark-gluon plasma in heavy-ion collisions was argued long ago [1] to enhance the strange particle production. While the significant strangeness yield enhancement has been experimentally observed in the central nucleus-nucleus collisions at CERN SPS (see the data compilation [2] and the recent review [3]), it is a matter of hot debate whether the observation can be indeed treated as a plasma signal. The strange hadron abundance is naturally described within the models assuming the plasma occurrence at the early collision stage (see e.g. [4,5]) but the models, which neglect such a possibility (see e.g. [6,7] or the review [8]), can be also tuned to agree with the experimental data. Thus, it would be desirable to go beyond the average particle numbers and see whether the strangeness enhancement in the central heavy-ion collisions is accompanied with the qualitative change of the strangeness yield fluctuations. The equilibrium quark-gluon plasma scenario is obviously expected to lead to the smaller fluctuations than the nonequilibrium cascade-like hadron models but the specific calculations are needed to quantify such a prediction. Anyhow, it seems to be really interesting to study the strangeness yield fluctuations on the event-by-event basis. However, we immediately face the difficulty how to quantitatively measure the fluctuations in the events of very different multiplicity. The problem appears to be of more general nature.There are several interesting proposals to use fluctuations as a potential source of valuable information on the collision dynamics. If the hadronic system produced in the collision is in the thermodynamical equilibrium, the temperature and multiplicity fluctuations have been argued to determine, respectively, the heat capacity [9,10] and compressibility [11] of the hadronic matter at freeze-out. An extensive discussion of the equilibrium fluctuations can be found in [12]. In the experimental realization of such ideas one has to disentangle however the 'dynamical' fluctuations of interest from the 'trivial' ge...