相対论的流体力学方程式98.ppt

相対論的流体力学方程式の微視的導出に関する最近の試み;Introduction;Fundamental problems with relativistic hydro-dynamical equations for viscous fluid ;Typical hydrodynamic equations for a viscous fluid ;Compatibility of the definitions of the flow and the nature of the Local Rest Frame;The separation of scales in the relativistic heavy-ion collisions;Relativistic Boltzmann equation;perturbation;Solution by the perturbation theory;1st;metric;fast motion;Application of RG/E equation to derive slow dynamics;References on the RG/E method:;The distribution function;;A generic form of the flow vector; ;Bulk viscosity Heat conductivity Shear viscosity ;;Which equation is better, Stewart et al’s or ours?;The Eckart and Grad-Marle-Stewart equations gives an instability, which has been known, and is now found to be attributed to the fluctuation-induced dissipation, proportional to . (ii) Our equation (TKO equation) seems to be stable, being dependent on the values of the transport coefficients and the EOS.;Compatibility with the underlying kinetic equations? ;Collision operator;The orthogonality condition due to the projection operator exactly corresponds to the constraints for the dissipative part of the energy-momentum tensor and the particle current!;Phenomenological Derivation;From;Energy frame:;Israel-Stewart equations fromKinetic equation on the basis of the RG method;Geometrical image of reductionof dynamics;The viscocities ;Summary;Backups;Fourier’s law; ;Five integral const’s；;with the initial cond.;;Up to 1st order;;Explicitly；;Example: Energy frame;Frame dependence of the relaxation times;B0y(v%s#oXlUiQfNbK8H5D2A+x*u$qZnWkShPeMaJ7F4C1z)wt!pYmVjRgOcL9I6E3B0y(v%r#oXlTiQfNbK8G5D2A-x*u$qZnVkShPdMaJ7F4C0z)ws!pYmUjRfOcL9H6E3B+y(u%r#oWlTiQeNbJ8G5D1A-x*t$qZnVkSgPdMaI7F4C0z)vs!pXmUjRfOcK9H6E2B+y(u%rZoWlThQeNbJ8G4D1A-w*t$qYnVjSgPdLaI7F3C0y)vs#pXmUiRfOcK9H5E2B+x(u%rZoWkThQeMbJ8G4D1z-w*t!qYnVjSgOdLaI6F3C0y)v%s#pXlUiRfNcK8H5E2A+x(u$rZnWkThPeM