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arXiv 1102.5485hep-phnucl-th
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用动态重整化群研究QCD临界点附近的动力学

Dynamics near QCD critical point by dynamic renormalization group

Yuki Minami

备注：
16 pages, 4 figures. accepted version by PRD. A comment on a frame dependence is added in Sec. V
发表信息：
Phys.Rev.D83:094019,2011
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摘要：

利用动力学重整化群对QCD临界点附近的动力学进行了基本分析。除了通过粗粒化的RG分析之外，我们构造了非线性朗之万方程作为临界动力学的基本方程。我们的构造是基于广义朗之万理论和相对论流体力学。将动态RG应用于所构造的方程，推导出输运系数的RG方程，并分析了它们的临界行为。我们发现，由此产生的RG方程原来是相同的液-气CP，除了一个微不足道的常数。因此，体粘滞系数和热导率在QCD CP处强烈发散。我们还表明，热扩散和粘性扩散模式表现出临界减慢与动态临界指数$z_{\rm thermal}\sim 3$和$z_{\rm viscous}\sim 2$，分别。相反，声传播模式显示出具有负指数$z_{\rm sound}\sim -0.8$的临界加速。

英文摘要：

We work out the basic analysis of dynamics near QCD critical point (CP) by dynamic renormalization group (RG). In addition to the RG analysis by coarse graining, we construct the nonlinear Langevin equation as a basic equation for the critical dynamics. Our construction is based on the generalized Langevin theory and the relativistic hydrodynamics. Applying the dynamic RG to the constructed equation, we derive the RG equation for the transport coefficients and analyze their critical behaviors. We find that the resulting RG equation turns out to be the same as that for the liquid-gas CP except for an insignificant constant. Therefore, the bulk viscosity and the thermal conductivity strongly diverge at the QCD CP. We also show that the thermal and viscous diffusion modes exhibit critical slowing down with the dynamic critical exponents $z_{\rm thermal}\sim 3$ and $z_{\rm viscous}\sim 2$, respectively. In contrast, the sound propagating mode shows critical speeding up with the negative exponent $z_{\rm sound}\sim -0.8$.

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