由模糊关联函数求取剪切粘度的稀疏建模方法
Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions
摘要：
我们提出了稀疏建模的方法来估计的谱函数从模糊的关联函数。本文描述了如何从梯度流方法（$C(t,τ)$）测量的有限温度淬火QCD的重整化能量动量张量（EMT）的关联函数中得到剪切粘滞系数。由于梯度流方法的拖尾特性，其重正化EMT的测量降低了统计不确定性。然而，拖影破坏了谱函数的求和规则，在物理观测量分析过程中，关联函数中的过拖影数据可能需要剔除。在这项工作中，我们证明了稀疏建模分析的中间表示基础（IR基础），它连接之间的松原频率数据和实际频率数据。即使仅在梯度流的基准窗口中使用非常有限的$C(t,τ)$数据，它也能很好地工作。我们利用ADMM算法，这是有用的，以解决LASSO问题在一定的约束。我们表明，得到的谱函数再现输入模糊的关联函数在有限的流动时间。还讨论了几个系统和统计误差和流量-时间依赖性。
英文摘要：
We propose the sparse modeling method to estimate the spectral function from the smeared correlation functions. We give a description of how to obtain the shear viscosity from the correlation function of the renormalized energy-momentum tensor (EMT) measured by the gradient flow method ($C(t,τ)$) for the quenched QCD at finite temperature. The measurement of the renormalized EMT in the gradient flow method reduces a statistical uncertainty thanks to its property of the smearing. However, the smearing breaks the sum rule of the spectral function and the over-smeared data in the correlation function may have to be eliminated from the analyzing process of physical observables. In this work, we demonstrate that the sparse modeling analysis in the intermediate-representation basis (IR basis), which connects between the Matsubara frequency data and real frequency data. It works well even using very limited data of $C(t,τ)$ only in the fiducial window of the gradient flow. We utilize the ADMM algorithm which is useful to solve the LASSO problem under some constraints. We show that the obtained spectral function reproduces the input smeared correlation function at finite flow-time. Several systematic and statistical errors and the flow-time dependence are also discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
