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Register a new userTransport coefficients of causal dissipative relativistic hydrodynamics in quenched lattice simulations
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Transport coefficients of causal dissipative relativistic fluid dynamics (CDR) are studied in quenched lattice simulations. CDR describes the behavior of relativistic non-Newtonian fluids in which the relaxation time appears as a new transport coefficient besides the shear and bulk viscosities. It was recently shown that these coefficients can be given by the temporal-correlation functions of the energy-momentum tensors as in the case of the Green-Kubo-Nakano formula. By using the new formula in CDR, we study the transport coefficients with lattice simulations in pure SU(3) gauge theory. After defining the energy-momentum tensor on the lattice, we extract a ratio of the shear viscosity to the relaxation time which is given only in terms of the static correlation functions. The simulations are performed on $24^3 times 4$--16 lattices with $beta_{_{rm LAT}} = 6.0$, which corresponds to the temperature range of $0.5 simle T/T_c simle 1.8$, where $T_c$ is the critical temperature.
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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 to apply to more general situations.
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 timescale exceeds half the transport mean free path tau0/lambda0 > ~2. The same accuracy with Navier-Stokes requires three times larger tau0/lambda0 > ~6. For dynamics driven by a constant cross section, on the other hand, about 50% larger tau0/lambda0 > ~3 (IS) and ~9 (NS) are needed. For typical applications at RHIC energies s_{NN}**(1/2) ~ 100-200 GeV, these limits imply that even the Israel-Stewart approach becomes marginal when eta/s > ~0.15. In addition, we find that the naive approximation to Israel-Stewart theory, which neglects products of gradients and dissipative quantities, has an even smaller range of applicability than Navier-Stokes. We also obtain analytic Israel-Stewart and Navier-Stokes solutions in 0+1D, and present further tests for numerical dissipative hydrodynamics codes in 1+1, 2+1, and 3+1D based on generalized conservation laws.
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.
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.
At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. Here, electromagnetic effects are included by superimposing $mathrm{U}(1)$ degrees of freedom on $N_f = 2+1$ QCD configurations from the Budapest-Marseille-Wuppertal Collaboration. We present preliminary results for the electromagnetic corrections to light pseudoscalars mesons masses and discuss some of the associated systematic errors.
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