String theory implications on causal hydrodynamics

Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality

We study causal hydrodynamics (Israel-Stewart theory) of gauge theory plasmas from the AdS/CFT duality. Causal hydrodynamics requires new transport coefficients (relaxation times) and we compute them for a number of supersymmetric gauge theories including the N=4 SYM. However, the relaxation times obtained from the "shear mode" do not agree with the ones from the "sound mode," which implies that the Israel-Stewart theory is not a sufficient framework to describe the gauge theory plasmas.

Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics

A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as…

相对论流体动力学的因果UV完备性

Causal UV completions of relativistic hydrodynamics

本文研究了相对论流体动力学的有效场论固有非因果性，并提出通过引入瞬时紫外模式来恢复因果性，同时探讨了非流体动力学模式的出现和限制。

Is first-order relativistic hydrodynamics in general frame stable and causal for arbitrary interaction?

We derive a first-order, stable and causal, relativistic hydrodynamic theory from the microscopic kinetic equation using the gradient expansion technique in a general frame. The general frame is introduced from the arbitrary matching conditions for hydrodynamic fields. The interaction is introduced in the relativistic Boltzmann equation through the momentum-dependent relaxation time approximation (MDRTA) with the proposed collision operator that preserves the conservation laws. We demonstrate here for the first time that not only the general frame choice, but also the momentum dependence of mi…

Stability and Causality in relativistic dissipative hydrodynamics

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.

最小因果自旋流体动力学的因果性与稳定性分析

Causality and stability analysis for the minimal causal spin hydrodynamics

本文对直到二阶的最小扩展自旋流体动力学进行了因果性与稳定性线性分析，证明一阶理论非因果且不稳定，推导了二阶最小因果自旋流体动力学的稳定性条件，并发现有限波矢处的稳定性破坏现象。

Causal dissipative hydrodynamics for heavy ion collisions

We briefly discuss the recent developments in causal dissipative hydrodynamic for relativistic heavy ion collisions. Phenomenological estimate of QGP viscosity over entropy ratio from several experimental data, e.g. STAR's $ϕ$ meson data, centrality dependence of elliptic flow, universal scaling elliptic flow etc. are discussed. QGP viscosity, extracted from hydrodynamical model analysis can have very large systematic uncertainty due to uncertain initial conditions.

因果且稳定的一阶手征流体动力学

Causal and stable first-order chiral hydrodynamics

本文推导一阶相对论手征流体动力学满足非线性因果性与线性稳定性的充要不等式，给出首个可证因果稳定的黏性理论，并将结果整理为适合数值模拟的形式。

Causality and stability analysis of first-order field redefinition in relativistic hydrodynamics from kinetic theory

In this work, the causality and stability of a first-order relativistic dissipative hydrodynamic theory, that redefines the hydrodynamic fields from a first principle microscopic estimation, have been analyzed. A generic approach of gradient expansion for solving the relativistic transport equation has been adopted using the Chapman-Enskog iterative method. Next, the momentum dependent relaxation time approximation (MDRTA) has been employed to quantify the collision term for analytical estimation of the field correction coefficients from kinetic theory. At linear regime, in local rest frame th…

Causal dissipative hydrodynamics obtained from the nonextensive/dissipative correspondence

We derive the constitutive equations of causal relativistic dissipative hydrodynamics ($d$-hydrodynamics) from perfect nonextensive hydrodynamics ($q$-hydrodynamics) using the nonextensive/dissipative correspondence (NexDC) proposed by us recently. The $q$-hydrodynamics can be thus regarded as a possible model for the $d$-hydrodynamics facilitating its application to high energy multiparticle production processes. As an example we have shown that applying the NexDC to the perfect 1+1 $q$-hydrodynamics, one obtains a proper time evolution of the bulk pressure and the Reynolds number.

Analytical solutions of causal relativistic hydrodynamic equations for Bjorken and Gubser flows

We obtain general analytical solutions of third-order viscous hydrodynamic equations for Bjorken and Gubser flows in systems with vanishing bulk viscosity and chemical potential, and having a constant shear relaxation time. We also analytically characterize and determine the hydrodynamic attractors for such systems by studying the universal behavior of these solutions at both early and late times. Finally we study the properties of these hydrodynamic attractors for transport coefficients obtained from relativistic kinetic theory in the relaxation-time approximation.

一阶共形各向异性流体力学中的因果性与稳定性

Causality and stability in first-order conformal anisotropic hydrodynamics

该研究构建了推广Bemfica-Disconzi-Noronha-Kovtun框架的相对论共形不带电流体一阶耗散各向异性流体力学理论，推导了因果性对输运系数的约束，验证了其因果稳定性，并应用于Bjorken流分析早期吸引子的约束条件。

Transport coefficients of Relativistic Causal Hydrodynamics for Hadrons

We investigate coefficients in the Israel-Stewart's causal hydrodynamics and discuss the way to calculate them with a microscopic theory. Based on the hadro-molecular simulation based on an event generator URASiMA, we evaluate the coefficients for a hot and dense hadronic fluid.

A systematic expansion for relativistic causal hydrodynamics

A systematic expansion of the Boltzmann equation for the diffusion of dilute tracers, in powers of the Knudsen number, carried out to next-to-leading order (NLO), gives the relativistic causal diffusion equation (Kelly's equation). Using dimensionless combinations of dynamical quantities, we show when the small NLO term plays a crucially important role. We proceed to show that a derivation of Kelly's equation from a microscopic theory of the correlation function of the number density of diffusers is possible. The correlator fulfils the Green-Kubo relation for the diffusion constant, as well as…

从超高速 boosts 中线性稳定性分析推导因果性必要条件

Necessary conditions for causality from linearized stability at ultra-high boosts

本文提出通过线性稳定性分析在非零动量下约束相对论流体系统的因果参数空间，利用洛伦兹不变稳定性性质，通过γ-抑制效应，在接近光速的 boosts 情况下，空间均匀极限下的稳定性准则可识别满足因果性必要条件的参数空间区域。

An expedition to the islands of stability in the first-order causal hydrodynamics

The recently proposed connection between the Lorentz invariance of stability and the speed of signal propagation has been tested for a first-order relativistic dissipative hydrodynamic theory. The fact that the stability situation in different reference frames agrees with each other only as long as the signal propagation respects causality, has been explicitly established for the theory, which is microscopically derived from the covariant kinetic equation in general hydrodynamic frames with arbitrary momentum-dependent interactions.

Second order causal hydrodynamics in Eckart frame: using gradient expansion scheme

In the present work, we develop a causal theory of relativistic non-ideal fluids up to the second order in the Eckart frame using gradient expansion scheme. Keeping the spirit of Mueller-Israel-Stewart formalism, the general forms of bulk viscosity, shear viscosity tensor and the heat flow vector are presented. Since each of the flux quantities explicitly carry curvature terms, we show that our formalism finds application in astrophysics in particular in the strong gravity regime. We elucidate two such applications namely in viscous thick accretion disks also known as Polish doughnuts and in a…

Microscopic formula for transport coefficients of causal hydrodynamics

The Green-Kubo-Nakano formula should be modified in relativistic hydrodynamics because of the problem of acausality and the breaking of sum rules. In this work, we propose a formula to calculate the transport coefficients of causal hydrodynamics based on the projection operator method. As concrete examples, we derive the expressions for the diffusion coefficient, the shear viscosity coefficient, and corresponding relaxation times.

Shock propagation and stability in causal dissipative hydrodynamics

We studied the shock propagation and its stability with the causal dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence of the usual viscosity is not enough to stabilize the solution. This problem is solved by introducing an additional viscosity which is related to the coarse-graining scale of the theory.

Local well-posedness in Sobolev spaces for first-order barotropic causal relativistic viscous hydrodynamics

We study the theory of relativistic viscous hydrodynamics introduced in arXiv:1109.0985 and arXiv:1907.12695, which provided a causal and stable first-order theory of relativistic fluids with viscosity in the case of barotropic fluids. The local well-posedness of its equations of motion has been previously established in Gevrey spaces. Here, we improve this result by proving local well-posedness in Sobolev spaces.

Equivalence between first-order causal and stable hydrodynamics and Israel-Stewart theory for boost-invariant systems with a constant relaxation time

We show that the recently formulated causal and stable first-order hydrodynamics has the same dynamics as Israel-Stewart theory for boost-invariant, Bjorken expanding systems with a conformal equation of state and a regulating sector determined by a constant relaxation time. In this case, the general solution of the new first-order formulation can be determined analytically.

具有守恒电荷的一阶相对论自旋流体动力学的因果性与稳定性

Causality and Stability of First-Order Relativistic Spin Hydrodynamics with Conserved Charges

研究具有粒子数守恒的一阶相对论自旋流体动力学的因果性与稳定性，通过推导色散关系发现守恒电荷动力学影响声区并引入新非流体动力学模式，粒子数诱导模式违反因果性，且守恒电荷未消除固有不稳定性，揭示了自旋与电荷动力学相互作用并提供理论约束。

Nonlinear causality of general first-order relativistic viscous hydrodynamics

Effective theory arguments are used to derive the most general energy-momentum tensor of a relativistic viscous fluid with an arbitrary equation of state (in the absence of other conserved currents) that is first-order in the derivatives of the energy density and flow velocity and does not include extended variables such as in Mueller-Israel-Stewart-like theories. This energy-momentum tensor leads to a causal theory, provided one abandons the usual conventions for the out-of-equilibrium hydrodynamic variables put forward by Landau-Lifshitz and Eckart. In particular, causality requires nonzero …

Fluctuations in Relativistic Causal Hydrodynamics

Formalism to calculate the hydrodynamic fluctuations by applying the Onsager theory to the relativistic Navier-Stokes equation is already known. In this work, we calculate hydrodynamic-fluctuations within the framework of the second order hydrodynamics of Müller, Israel and Stewart and its generalization to the third order. We have also calculated the fluctuations for several other causal hydrodynamical equations. We show that the form for the Onsager-coefficients and form of the correlation-functions remains same as those obtained by the relativistic Navier-Stokes equation and it does not dep…

Causal relativistic hydrodynamics for viscous fluids

We report on recent results from VISH2+1, a code that solves the relativistic Israel-Stewart equations for causal viscous hydrodynamics for heavy-ion collisions with longitudinal boost invariance. We find that even ``minimal'' shear viscosity eta/s=hbar/(4pi) leads to a large reduction of elliptic flow compared to ideal fluid dynamics. We explore systematically the sensitivity of this reduction to the equation of state, system size, initial conditions, and the microscopic relaxation time in different formulations of the Israel-Stewart equations.

Causal Viscous Hydrodynamics for Central Heavy-Ion Collisions

We study causal viscous hydrodynamics in the context of central relativistic heavy-ion collisions and provide details of a straightforward numerical algorithm to solve the hydrodynamic equations. It is shown that correlation functions of fluctuations provide stringent test cases for any such numerical algorithm. Passing these tests, we study the effects of viscosity on the temperature profile in central heavy-ion collisions. Also, we find that it is possible to counter-act the effects of viscosity to some extent by re-adjusting the initial conditions. However, viscous corrections are strongest…

Effects of bulk viscosity on hadron spectra and Hanbury-Brown Twiss radius by the causal viscous hydrodynamics

The particle spectra and Hanbury-Brown Twiss (HBT) radius of Au+Au collisions at RHIC energy are investigated by a hydrodynamical expanding source with both shear and bulk viscosities ($ζ$). With a large width of the ratio of $ζ$ to entropy density $s$, both the particle transverse momentum spectra and the ratio $R_{out}/R_{side}$ of HBT radii in the direction of the total transverse momentum of detected two particles ($R_{out}$) and perpendicular to both this direction and the beam direction ($R_{side}$) become a little steeper.

Rapidity Correlation Structures from Causal Hydrodynamics

Viscous diffusion can broaden the rapidity dependence of two-particle transverse momentum fluctuations. Surprisingly, measurements at RHIC by the STAR collaboration demonstrate that this broadening is accompanied by the appearance of unanticipated structure in the rapidity distribution of these fluctuations in the most central collisions. Although a first order classical Navier-Stokes theory can roughly explain the rapidity broadening, it cannot explain the additional structure. We propose that the rapidity structure can be explained using the second order causal Israel-Stewart hydrodynamics w…

Causal Viscous Hydrodynamics for Relativistic Heavy Ion Collisions

The viscosity of the QGP is a presently hotly debated subject. Since its computation from first principles is difficult, it is desirable to try to extract it from experimental data. Viscous hydrodynamics provides a tool that can attack this problem and which may work in regions where ideal hydrodynamics begins to fail. This thesis focuses on viscous hydrodynamics for relativistic heavy ion collisions. We first review the 2nd order viscous equations obtained from different approaches, and then report on the work of the Ohio State University group on setting up the equations for causal viscous h…

Relativistic Dissipative Hydrodynamics: A Minimal Causal Theory

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.

Stability of 1+1 dimensional causal relativistic viscous hydrodynamics

The stability of the 1+1 dimensional solution of Israel-Stewart theory is investigated. Firstly, the evolution of the temperature and the ratio of the bulk pressure over the equilibrium pressure of the background is explored. Then the stability with linear perturbations is studied by using the Lyapunov direct method. It shows that the shear viscosity may weaken the instability induced by the large peak of bulk viscosity around the phase transition temperature $T_c$.

Causal Viscous Hydrodynamics for Central Heavy-Ion Collisions II: Meson Spectra and HBT Radii

Causal viscous hydrodynamic fits to experimental data for pion and kaon transverse momentum spectra from central Au+Au collisions at \sqrt{s_{NN}}=200 GeV are presented. Starting the hydrodynamic evolution at 1 fm/c and using small values for the relaxation time, reasonable fits up to moderate ratios η/s\simeq 0.4 can be obtained. It is found that a percentage of roughly 50 η/s to 75 η/s of the final meson multiplicity is due to viscous entropy production. Finally, it is shown that with increasing viscosity, the ratio of HBT radii R_{out}/R_{side} approaches and eventually matches the experime…

相对论流体力学的因果菱形

The causal diamond of relativistic hydrodynamics

本文指出传统泰勒展开诊断流体动力学收敛性可能失效，提出在壳外构成关系层面研究梯度展开，建立因果菱形收敛区域，并揭示非流体动力学谱的获取途径。

Causal, stable first-order viscous relativistic hydrodynamics with ideal gas microphysics

We present the first numerical analysis of causal, stable first-order relativistic hydrodynamics with ideal gas microphysics, based in the formalism developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK approach provides definitions for the conserved stress-energy tensor and baryon current, and rigorously proves causality, local well-posedness, strong hyperbolicity, and linear stability (about equilibrium) for the equations of motion, subject to a set of coupled nonlinear inequalities involving the undetermined model coefficients (the choice for which defines the "hydrody…

膨胀系统中因果流体动力学涨落的动力学

Dynamics of causal hydrodynamic fluctuations in an expanding system

该研究在一维膨胀系统中构建因果流体动力学涨落框架并围绕boost不变解线性化，揭示热力学变量结构近乎冻结的现象，并阐明末态强子两粒子关联与强子质量及介质性质的关系。

相对论性流体动力学涨落的有效作用量：因果性、稳定性与信息流

Relativistic hydrodynamic fluctuations from an effective action: causality, stability, and the information current

本文通过有效作用量研究相对论流体动力学涨落，证明因果性与稳定性约束一阶BDNK和二阶Israel-Stewart理论的关联函数，并发现修正的Kubo-Martin-Schwinger对称性，为流体动力学有效作用量提供新指导。

Causal hydrodynamic fluctuations in non-static and inhomogeneous backgrounds

To integrate hydrodynamic fluctuations, namely thermal fluctuations of hydrodynamics, into dynamical models of high-energy nuclear collisions based on relativistic hydrodynamics, the property of the hydrodynamic fluctuations given by the fluctuation-dissipation relation should be carefully investigated. The fluctuation-dissipation relation for causal dissipative hydrodynamics with the finite relaxation time is naturally given in the integral form of the constitutive equation by the linear-response theory. While, the differential form of the constitutive equation is commonly used in analytic in…

Causal dissipative hydrodynamics for QGP fluid in 2+1 dimensions

In 2nd order causal dissipative theory, space-time evolution of QGP fluid is studied in 2+1 dimensions. Relaxation equations for shear stress tensors are solved simultaneously with the energy-momentum conservation equations. Comparison of evolution of ideal and viscous QGP fluid, initialized under the same conditions, e.g. same equilibration time, energy density and velocity profile, indicate that in a viscous dynamics, energy density or temperature of the fluid evolve slowly, than in an ideal fluid. Cooling gets slower as viscosity increases. Transverse expansion also increases in a viscous d…

Schwinger-Keldysh有效场论用于稳定且因果的相对论流体动力学

Schwinger-Keldysh effective field theory for stable and causal relativistic hydrodynamics

本文构建了稳定且因果的有效场论，用于描述相对论扩散和流体动力学中的统计涨落，实现动力学KMS对称性，并指出在BDNK模型中包含涨落的障碍。

Correspondence between Israel-Stewart and first-order causal and stable hydrodynamics for Bjorken-expanding baryon-rich systems with vanishing particle masses

We obtain an exact correspondence between the dynamical equations in Israel-Stewart (IS) theory and first-order causal and stable (FOCS) hydrodynamics for a boost-invariant system with an ideal gas equation of state at finite baryon chemical potential. Explicit expressions for the temperature and chemical potential dependence of the regulators in the FOCS theory are given in terms of the kinetic coefficients and constant relaxation time of the IS theory. Using the correspondence between the IS and FOCS theory, stability conditions for a charged fluid which are known in the FOCS approach are ap…

Aspects of causal viscous hydrodynamics

We investigate the phenomenology of freely expanding fluids, with different material properties, evolving through the Israel-Stewart (IS) causal viscous hydrodynamics, and compare our results with those obtained in the relativistic Eckart-Landau-Navier-Stokes (ELNS) acausal viscous hydrodynamics. Through the analysis of scaling invariants we give a definition of thermalization time which can be self-consistently determined in viscous hydrodynamics. Next we construct the solutions for one-dimensional boost-invariant flows. Expansion of viscous fluids is slower than that of one-dimensional ideal…

Effects of causality on the fluidity and viscous horizon of quark-gluon plasma

The second order Israel-Stewart-M$\ddot{u}$ller relativistic hydrodynamics has been applied to study the effects of causality on the acoustic oscillation in relativistic fluid. Causal dispersion relations have been derived with non-vanishing shear viscosity, bulk viscosity and thermal conductivity at non-zero temperature and chemical potential. These relations have been used to investigate the fluidity of Quark Gluon Plasma (QGP) at finite temperature ($T$). Results of the first order dissipative hydrodynamics have been obtained as limiting case of the second order theory. The effects of the c…

一阶因果且稳定相对论流体力学中涨落的一致纳入

Consistent inclusion of fluctuations in first-order causal and stable relativistic hydrodynamics

本文首次构建了线性随机涨落的 BDNK 理论，证明其数学一致、因果且协变稳定，并揭示了非流体力学模式导致的长程关联及与 Israel-Stewart 理论之间的非局域变量变换关系。

富含重子的Israel-Stewart流体动力学的非线性因果性与强双曲性

Nonlinear causality and strong hyperbolicity of baryon-rich Israel-Stewart hydrodynamics

该研究提出首组完全非线性充要条件，可保证含切变与体粘滞、耦合非零重子流的Israel-Stewart流体动力学初值的因果演化与强双曲性，为相关天体物理与核物理研究奠定数学基础。

Extensivity of Irreversible Current and Stability in Causal Dissipative Hydrodynamics

We extended our formulation of causal dissipative hydrodynamics [T. Koide \textit{et al.}, Phys. Rev. \textbf{C75}, 034909 (2007)] to be applicable to the ultra-relativistic regime by considering the extensiveness of irreversible currents. The new equation has a non-linear term which suppresses the effect of viscosity. We found that such a term is necessary to guarantee the positive definiteness of the inertia term and stabilize numerical calculations in ultra-relativistic initial conditions. Because of the suppression of the viscosity, the behavior of the fluid is more close to that of the id…

因果且稳定的相对论流体力学涨落

Causal and Stable Relativistic Hydrodynamic Fluctuations

本文提出一种计算相对论流体力学系统噪声关联子的新方法，并将其应用于一般框架下的 Israel-Stewart 理论，以判断流体力学框架是否与热涨落一致。

String-Theory-Based Predictions for Nonhydrodynamic Collective Modes in Strongly Interacting Fermi Gases

Very different strongly interacting quantum systems such as Fermi gases, quark-gluon plasmas formed in high energy ion collisions and black holes studied theoretically in string theory are known to exhibit quantitatively similar damping of hydrodynamic modes. It is not known if such similarities extend beyond the hydrodynamic limit. Do non-hydrodynamic collective modes in Fermi gases with strong interactions also match those from string theory calculations? In order to answer this question, we use calculations based on string theory to make predictions for novel types of modes outside the hydr…

New developments in relativistic hydrodynamics

We review recent progress in relativistic hydrodynamics, discussing causal and stable first-order hydrodynamics, known as BDNK theories, hydrodynamic attractors, as well as hydrodynamics near the chiral critical point and spin hydrodynamics.

二阶自旋流体力学中静止系模式的稳定性与因果性

Stability and causality of rest frame modes in second-order spin hydrodynamics

本文分析二阶自旋流体力学静止系模式的稳定性与因果性，提出含40个弛豫方程的 Israel-Stewart 截断方案，并指出需满足广义 Frenkel 条件。

Dilepton production in a schematic causal viscous hydrodynamics

Assuming that in the hot dense matter produced in relativistic heavy-ion collisions, the energy density, entropy density, and pressure as well as the azimuthal and space-time rapidity components of the shear tensor are uniform in the direction transversal to the reaction plane, we derive a set of schematic equations from the Isreal-Stewart causal viscous hydrodynamics. These equations are then used to describe the evolution dynamics of relativistic heavy-ion collisions by taking the shear viscosity to entropy density ratio of $1/4π$ for the initial quark-gluon plasma (QGP) phase and of ten tim…

Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions

We explore the effects of shear viscosity on the hydrodynamic evolution and final hadron spectra of Cu+Cu collisions at ultrarelativistic collision energies, using the newly developed (2+1)-dimensional viscous hydrodynamic code VISH2+1. Based on the causal Israel-Stewart formalism, this code describes the transverse evolution of longitudinally boost-invariant systems without azimuthal symmetry around the beam direction. Shear viscosity is shown to decelerate the longitudinal and accelerate the transverse hydrodynamic expansion. For fixed initial conditions, this leads to a longer quark-gluon p…

参考系变换与稳定-因果流体动力学理论

Frame transformation and stable-causal hydrodynamic theory

本研究指出了相对论流体动力学理论不同表述间的联系，通过线性化全阶梯度修正将 BDNK 应力张量改写至 Landau 参考系，证明其等价于含无限阶导数或 MIS 型非流体变量的系统，并验证了色散关系的一致性。

A Fast Numerical Scheme for Causal Relativistic Hydrodynamics with Dissipation

In this paper, we develop a stable and fast numerical scheme for relativistic dissipative hydrodynamics based on Israel-Stewart theory. Israel-Stewart theory is a stable and causal description of dissipation in relativistic hydrodynamics although it includes relaxation process with the timescale for collision of constituent particles, which introduces stiff equations and makes practical numerical calculation difficult. In our new scheme, we use Strang's splitting method, and use the piecewise exact solutions for solving the extremely short timescale problem. In addition, since we split the cal…

The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions

We utilize nonequilibrium covariant transport theory to determine the region of validity of causal Israel-Stewart dissipative hydrodynamics (IS) and Navier-Stokes theory (NS) for relativistic heavy ion physics applications. A massless ideal gas with 2->2 interactions is considered in a 0+1D Bjorken scenario, appropriate for the early longitudinal expansion stage of the collision. In the scale invariant case of a constant shear viscosity to entropy density ratio eta/s ~ const, we find that Israel-Stewart theory is 10% accurate in calculating dissipative effects if initially the expansion timesc…