Thermalization of Green functions and quasinormal modes
Thermalization of Green functions and quasinormal modes
复制标题
格林函数和拟正规模式的热化
DOI：
10.1007/jhep07(2015)041
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发表时间：
2015
影响因子：
5.4
通讯作者：
Surbhi Khetrapal
中科院分区：
文献类型：
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作者：
J. R. David;Surbhi Khetrapal
本文发展了一种新的方法来研究与薄壳AdS Vaidya时空全息对偶的共形场论中含时延迟绿色函数的热化。该方法依赖于使用的所有时间导数的绿色函数在壳的信息，然后将其演变为以后的时间。用递推公式给出了绿色函数在壳体处的时间导数。利用这种方法，我们得到了绿色函数短时热化的解析结果。我们表明，晚的时间行为的绿色函数是由第一拟正规模式。然后，我们实现了数值方法。作为该方法的应用，我们研究了AdS 3和AdS 5薄Vaidya壳中与极小耦合标量对应的滞后时间相关绿色函数的热化问题。我们看到，正如预期的那样，后期的行为是由第一个拟正规模式决定的。我们应用该方法研究了AdS5 Vaidya壳的剪切矢量模式的后期行为。在小的动量，相应的时间依赖的绿色功能预计将松弛平衡的剪切流体动力学模式。利用这一点，我们得到的剪切粘度的熵密度从一个时间依赖性的过程的普适比。
We develop a new method to study the thermalization of time dependent retarded Green function in conformal field theories holographically dual to thin shell AdS Vaidya space times. The method relies on using the information of all time derivatives of the Green function at the shell and then evolving it for later times. The time derivatives of the Green function at the shell is given in terms of a recursion formula. Using this method we obtain analytic results for short time thermalization of the Green function. We show that the late time behaviour of the Green function is determined by the first quasinormal mode. We then implement the method numerically. As applications of this method we study the thermalization of the retarded time dependent Green function corresponding to a minimally coupled scalar in the AdS3 and AdS5 thin Vaidya shells. We see that as expected the late time behaviour is determined by the first quasinormal mode. We apply the method to study the late time behaviour of the shear vector mode in AdS5 Vaidya shell. At small momentum the corresponding time dependent Green function is expected to relax to equilibrium by the shear hydrodynamic mode. Using this we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process.