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arXiv 1010.4359nucl-thcond-mat.stat-mechhep-phphysics.flu-dyn
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因果耗散相对论流体动力学的体粘滞系数和弛豫时间

Bulk Viscosity and Relaxation Time of Causal Dissipative Relativistic Fluid Dynamics

Xu-Guang Huang, Takeshi Kodama, Tomoi Koide, Dirk H. Rischke

备注：
23 pages, 2 figures
发表信息：
Phys.Rev.C83:024906,2011
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摘要：

利用投影算符方法导出了因果耗散相对论流体动力学中体粘滞系数$ζ$和相应的弛豫时间$τ_Π$的微观表达式。在将这些公式应用于π介子流体时，我们发现，为了得到一致的结果，应该采用可重整化的能量动量张量。在手征微扰理论的首阶近似下，弛豫时间在QCD相变附近增强，$τ_Π$和$ζ$关系为$τ_Π=ζ/[β\{(1/3-c_{s}^{2})(ε+P)-2(ε-3P)/9\}]$，其中$ε$、$P$和$c_{s}$分别为能量密度、声压和声速.预测的$ζ$和$% τ_Π$应满足所谓的因果关系条件。我们将我们的结果与Israel和Stewart的动力学计算结果以及弦理论的结果进行了比较，并确认这三种方法都符合因果关系条件。

英文摘要：

The microscopic formulae of the bulk viscosity $ζ$ and the corresponding relaxation time $τ_Π$ in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulae 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 $τ_Π$ and $ζ$ are related as $τ_Π=ζ/[β\{(1/3-c_{s}^{2})(ε+P)-2(ε-3P)/9\}]$, where $ε$, $P$ and $c_{s}$ are the energy density, pressure and velocity of sound, respectively. The predicted $ζ$ and $% τ_Π$ 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 the three approaches are consistent with the causality condition.

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