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arXiv 1105.2483hep-thcond-mat.stat-mechhep-phnucl-th
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有限温度和化学势下因果耗散相对论流体动力学的剪切粘度、体积粘度和弛豫时间

Shear viscosity, Bulk viscosity and Relaxation Times of Causal Dissipative Relativistic Fluid-Dynamics at Finite Temperature and Chemical Potential

Xu-Guang Huang, Tomoi Koide

备注：
v3:26 pages, 4 figures, published version
发表信息：
Nucl. Phys. A889, 73 (2012)
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摘要：

利用投影算符方法，在有限温度和有限化学势下，得到了因果耗散相对论流体动力学的剪切粘度$η$、体粘度$ζ$以及相应的弛豫时间$τ_π$和$τ_Π$的微观表达式.有限化学势计算的非平凡性归因于体粘滞压力算子定义的任意性，我们表明，当体粘滞压力算子定义$Π$选择适当时，其比值$ζ$/$τ_Π$的首阶结果与化学势为零时得到的比值一致.我们进一步讨论了记忆函数的无时间卷积近似的物理意义，并采用它导出了主要公式。我们发现TCL近似适当地违反了时间反演对称性，并导致与van Hove得到的量子主方程一致的结果。此外，这种近似可以重现的传输系数的精确关系，通过使用由Kadanoff和Martin导出的f-和规则。我们的方法也可以重现Baier等人的结果。（2008）参考\cite{con}，通过考虑TCL近似的下一阶校正，尽管该校正引起若干问题。

英文摘要：

The microscopic formulas for the shear viscosity $η$, the bulk viscosity $ζ$, and the corresponding relaxation times $τ_π$ and $τ_Π$ of causal dissipative relativistic fluid-dynamics are obtained at finite temperature and chemical potential by using the projection operator method. The non-triviality of the finite chemical potential calculation is attributed to the arbitrariness of the operator definition for the bulk viscous pressure.We show that, when the operator definition for the bulk viscous pressure $Π$ is appropriately chosen, the leading-order result of the ratio, $ζ$ over $τ_Π$, coincides with the same ratio obtained at vanishing chemical potential. We further discuss the physical meaning of the time-convolutionless (TCL) approximation to the memory function, which is adopted to derive the main formulas. We show that the TCL approximation violates the time reversal symmetry appropriately and leads results consistent with the quantum master equation obtained by van Hove. Furthermore, this approximation can reproduce an exact relation for transport coefficients obtained by using the f-sum rule derived by Kadanoff and Martin. Our approach can reproduce also the result in Baier et al.(2008) Ref. \cite{con} by taking into account the next-order correction to the TCL approximation, although this correction causes several problems.

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