We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

We show that the pseudogap of the quark density of states is formed in hot quark matter as a precursory phenomenon of the color superconductivity on the basis of a low-energy effective theory. We clarify that the soft mode of the di-quark pair field gives rise to a peculiar behavior of the quark dispersion relation and a short life-time of the quasiparticles near the Fermi surface, both of which make a depression of the density of states of quarks. Our result suggests that the appearance of the pseudogap is a universal phenomenon of strong coupling superconductors, irrespective of the dimensionality.Comment: 4 pages, 4 figures, PTPTeX; Proceedings of Finite Density QCD at Nara July 10-12 2003 Nara Prefecture Public Hall Big Roof Nara Japan; v2:errors in affiliation are correcte

The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed. We show that the problem of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.

We review several facets of the hydrodynamic description of the relativistic heavy ion collisions, starting from the historical motivation to the present understandings of the observed collective aspects of experimental data, especially those of the most recent RHIC and LHC results. In this report, we particularly focus on the conceptual questions and the physical foundations of the validity of the hydrodynamic approach itself. We also discuss recent efforts to clarify some of the points in this direction, such as the various forms of derivations of relativistic hydrodynamics together with the limitations intrinsic to the traditional approaches, variational approaches, known analytic solutions for special cases, and several new theoretical developments. Throughout this review, we stress the role of course-graining procedure in the hydrodynamic description and discuss its relation to the physical observables through the analysis of a hydrodynamic mapping of a microscopic transport model. Several questions to be answered to clarify the physics of collective phenomena in the relativistic heavy ion collisions are pointed out.

We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic dissipative fluid dynamics are always stable. We then perform a linear stability analysis in a Lorentz-boosted frame. Provided that the ratio of the relaxation time for the shear stress tensor, τ π , to the sound attenuation length, Γ s = 4η/3(ε + P ), fulfills a certain asymptotic causality condition, the equations of motion give rise to stable solutions.Although the group velocity associated with perturbations may exceed the velocity of light in a certain finite range of wavenumbers, we demonstrate that this does not violate causality, as long as the asymptotic causality condition is fulfilled. Finally, we compute the characteristic velocities and show that they remain below the velocity of light if the ratio τ π /Γ s fulfills the asymptotic causality condition.

We present a new formalism for the theory of relativistic dissipative hydrodynamics. Here, we look for the minimal structure of such a theory which satisfies the covariance and causality by introducing the memory effect in irreversible currents. Our theory has a much simpler structure and thus has several advantages for practical purposes compared to the Israel-Stewart theory (IS).It can readily be applied to the full three-dimensional hydrodynamical calculations. We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.

In this work, we examine the effect of bulk viscosity on elliptic flow, taking into account the critical behavior of the equation of state and transport coefficients near the QCD phase transition. We found that the p T dependence of v 2 is quantitatively changed by the presence of the QCD phase transition. Within reasonable values of the transport coefficients, v 2 decreases by a factor of 15% at small p T values (<1 GeV). However, for larger values of p T (>2 GeV), the interplay between the velocity of sound and transport coefficient near the QCD phase transition enhances v 2 . We point out that Grad's 14-moment approximation cannot be applied for the calculation of the one-particle distribution function at the freeze-out. A. Memory function method in a hyperbolic coordinate systemAs is well known, the application of dissipative hydrodynamics in the relativistic regime requires some caution. Recently, it became clear that the instability of the hydrodynamic

We investigate the possible precursory phenomena of color superconductivity in quark matter at finite temperature T with use of a low-energy effective theory of QCD. It is found that the fluctuating pair field exists with a prominent strength even well above the critical temperature T c . We show that the collective pair field has a complex energy located in the second Riemann sheet, which approaches the origin as T is lowered to T c . We discuss the possible relevance of the precursor to the observables to be detected in heavy ion collisions.It is an intriguing subject to explore how the QCD vacuum changes in hot and dense hadronic matter ͓1,2͔. The recent lattice QCD simulations ͓3͔ show that the QCD vacuum undergoes a phase transition to a chirally restored and deconfined phase at low temperature ͑T͒ as T ϳ170 MeV. Although it is still a great challenge to perform a Monte Carlo simulation with a finite chemical potential on lattice QCD with an SU͑3͒ color group, we believe that a chirally restored and deconfined system is realized in dense hadronic matter with large .It is to be noticed that a system with a finite at low T can have a Fermi surface and the system may be described as a Fermi liquid composed of quarks. In accordance with the validity of the diquark-quark picture of baryons ͓4͔, the quark-quark interaction is attractive in some specific channels. Then the existence of the Fermi surface gives rise to a Cooper instability with respect to the formation of the diquark or Cooper pair in the most attractive channel, and the system is rearranged to a superconducting phase where the color-gauge symmetry is dynamically broken ͓5͔. Such color superconductivity ͑CSC͒ has recently acquired renewed interest, because the resulting gap ⌬ was shown to be as large as 100 MeV ͓6,7͔. Furthermore, the color and flavor degrees of freedom of quarks give a fantastically rich structure in dense quark matter with CSC ͓8͔: Such quark matter may be realized in the deep interior of neutron stars ͑NS͒, and characteristic phenomena observed for NS such as the glitch phenomena might be attributed to the existence of the CSC in the NS.Can CSC be relevant to experiments in the laboratory on Earth? The experiment using the available facilities, such as the BNL Relativistic Heavy Ion Collider ͑RHIC͒ using high energy heavy ion collisions seems unfortunately unfit for the problem, because the matter produced by RHIC is almost baryon-free with much higher temperatures than the critical temperature T c ϳ50-60 MeV of CSC. The purpose of the present paper is to explore possible precursory phenomena of CSC at TϾT c , i.e., in the Wigner phase and show that the fluctuation of the pair field is significant at T well above T c , which thereby might affect observables to be detected by the heavy ion collisions with large baryon stopping ͓9͔.Since we are interested in relatively the low T and region, we adopt a low-energy effective theory of QCD as was done in ͓6,10͔ where an instanton-induced interaction is employed. We remark here that a si...