Chromohydrodynamic approach to the unstable quark-gluon plasma

Abstract

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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Shear viscosity η to electrical conductivity σel ratio for an anisotropic QGP

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