Tomoi Koide

Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory

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 latters 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.

Effect of bulk viscosity on elliptic flow near the QCD phase transition

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{sub T} dependence of v{sub 2} is quantitatively changed by the presence of the QCD phase transition. Within reasonable values of the transport coefficients, v{sub 2} decreases by a factor of 15% at small p{sub T} values ( 2 GeV), the interplay between the velocity of sound and transport coefficient near the QCD phase transition enhances v{sub 2}. We point out that Grads 14-moment approximation cannot be applied for the calculation of the one-particle distribution function at the freeze-out.

Does stability of relativistic dissipative fluid dynamics imply causality

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 {tau}{sub {pi}}to the sound attenuation length {Gamma}{sub s}=4{eta}/3({epsilon}+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 wave numbers, 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 {tau}{sub {pi}/{Gamma}s} fulfills the asymptotic causality condition.

The effect of shear and bulk viscosities on elliptic flow

In this work, we examine the effect of shear and bulk viscosities on elliptic flow by taking a realistic parameterization of the shear and bulk viscous coefficients, η and ζ, and their respective relaxation times, τπ and τΠ. We argue that the behaviors close to an ideal fluid observed at RHIC energies may be related to the non-trivial temperature dependence of these transport coefficients.

Bulk viscosity and relaxation time of causal dissipative relativistic fluid dynamics

The microscopic formulas of the bulk viscosity {zeta} and the corresponding relaxation time {tau}{sub {Pi}} in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulas to the pionic fluid, we find that the renormalizable energy-momentum tensor should be employed to obtain consistent results. In the leading-order approximation in the chiral perturbation theory, the relaxation time is enhanced near the QCD phase transition, and {tau}{sub {Pi}} and {zeta} are related as {tau}{sub {Pi}={zeta}}/[{beta}{l_brace}(1/3-c{sub s}{sup 2})({epsilon}+P)-2({epsilon}-3P)/9{r_brace}], where {epsilon}, P, and c{sub s} are the energy density, pressure, and velocity of sound, respectively. The predicted {zeta} and {tau}{sub {Pi}} should satisfy the so-called causality condition. We compare our result with the results of the kinetic calculation by Israel and Stewart and the string theory, and confirm that all three approaches are consistent with the causality condition.

Consistency of field-theoretical and kinetic calculations of viscous transport coefficients for a relativistic fluid

Abstract We investigate the ratios β η ≡ η / τ π and β ζ ≡ ζ / τ Π , i.e., the ratios of shear, η , and bulk, ζ , viscosities to the relaxation times τ π , τ Π of the shear stress tensor and bulk viscous pressure, respectively, in the framework of causal relativistic dissipative fluid dynamics. These viscous transport coefficients are computed both in a field-theoretical and a kinetic approach based on the Boltzmann equation. Our results differ from those of the traditional Boltzmann calculation by Israel and Stewart. The new expressions for the viscous transport coefficients agree with the results obtained in the field-theoretical approach when the contributions from pair annihilation and creation (PAC) are neglected. The latter induce non-negligible corrections to the viscous transport coefficients.

Non‐Newtonian Properties of Relativistic Fluids

We show that relativistic fluids behave as non‐Newtonian fluids. First, we discuss the problem of acausal propagation in the diffusion equation and introduce the modified Maxwell‐Cattaneo‐Vernotte (MCV) equation. By using the modified MCV equation, we obtain the causal dissipative relativistic (CDR) fluid dynamics, where unphysical propagation with infinite velocity does not exist. We further show that the problems of the violation of causality and instability are intimately related, and the relativistic Navier‐Stokes equation is inadequate as the theory of relativistic fluids. Finally, the new microscopic formula to calculate the transport coefficients of the CDR fluid dynamics is discussed. The result of the microscopic formula is consistent with that of the Boltzmann equation, i.e., Grad’s moment method.

Causality and stability of dissipative fluid dynamics with diffusion currents

We analyze the causality and stability of the fluid dynamics with diffusion currents. We compute the dispersion relation in the local rest frame and Lorentz boost one. We obtain the asymptotic causality condition in the large wave number limit. If this condition is fulfilled, the system is always stable in any frame. We also find that the divergence in the group velocity is similar to the shear modes.

OPEN PROBLEMS IN THE HYDRODYNAMICAL APPROACH TO RELATIVISTIC HEAVY ION COLLISIONS

We discuss some open problems in hydrodynamical approach to the relativistic heavy ion collisions. In particular, we propose a new, very simple alternative approach to the relativistic dissipative hydrodynamics of Israel and Stewart.

Langevin Dynamics of Chiral Phase Transition at Finite Temperature and Density

We derive the linear Langevin equation to describe the dynamics of the chiral phase transition above the critical temperature by applying the projection operator method to the Nambu‐Jona‐Lasinio model at finite temperature and density. The relaxation time of the critical fluctuations increases as the temperature approaches toward the critical temperature because of the critical slowing down. The critical slowing down is enhanced in low temperature and large chemical potential region and around the tricritical point.