相対论的流体力学方程式.pptVIP

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相対论的流体力学方程式

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 13th Heavy-Ion Café  「相対論的流体力学と高エネルギー重イオン反応:来し方行く末」  2009年11月14日, 東大理 Introduction Relativistic hydrodynamics for a perfect fluid is widely and successfully used in the RHIC phenomenology. T. Hirano, D.Teaney, … . A growing interest in dissipative hydrodynamics. hadron corona (rarefied states); Hirano et al … Generically, an analysis using dissipative hydrodynamics is needed even to show the dissipative effects are small. The separation of scales in the relativistic heavy-ion collisions Liouville Boltzmann Fluid dyn. Hamiltonian   References on the RG/E method: T.K. Prog. Theor. Phys. 94 (’95), 503; 95(’97), 179 T.K.,Jpn. J. Ind. Appl. Math. 14 (’97), 51 T.K.,Phys. Rev. D57 (’98),R2035 T.K. and J. Matsukidaira, Phys. Rev. E57 (’98), 4817 S.-I. Ei, K. Fujii and T.K., Ann. Phys. 280 (2000), 236 Y. Hatta and T. Kunihiro, Ann. Phys. 298 (2002), 24 T.K. and K. Tsumura, J. Phys. A: Math. Gen. 39 (2006), 8089 (hep-th/0512108) K. Tsumura, K. Ohnishi and T.K., Phys. Lett. B646 (2007), 134 Compatibility with the underlying kinetic equations? Eckart constraints are not compatible with the Boltzmann equation, as proved in K.Tsumura, T.K. and K.Ohnishi;PLB646 (’06), 134. Israel-Stewart equations from Kinetic equation on the basis of the RG method Geometrical image of reduction of dynamics Summary The (dynamical) RG method is applied to derive generic 1st- and 2nd-order fluid dynamic equations, giving new constraints in the particle frame, consistent with a general phenomenological derivation. The new equation in the particle frame does not show a pathological behavior as Eckart eq. does. This means that the acausality problem and instability problem are due to different origins, respectively. Backups 轿曳矢萨碓东讯裎鎏碓悍矢工渌蹑室坌宄钵镅鹋藏究蛘炙肭凵拗钡磐舍仗梨蹿蛹堞 Fourier’s law; Then Causality is broken; the signal propagate with an infinite speed. Modification; Nonlocal thermodynamics Memory effec

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