论文标题
稀疏建模方法是从涂抹相关函数中获得剪切粘度的
Sparse modeling approach to obtaining the shear viscosity from smeared correlation functions
论文作者
论文摘要
我们提出了稀疏的建模方法，以估算污迹相关函数的光谱函数。我们给出了如何从有限温度下通过梯度流量法（$ c（t，τ）$）测量的重量化能量量张量（EMT）的相关函数的剪切粘度的描述。梯度流量方法中重新归一化的EMT的测量得益于其涂抹的特性，可降低统计不确定性。但是，涂抹破坏了光谱函数的总和规则，并且相关函数中的过度数据可能必须从物理可观察物的分析过程中消除。在这项工作中，我们证明了中间代理基础（IR基础）的稀疏建模分析，该分析在Matsubara频率数据和实际频率数据之间连接。它即使使用$ C（T，τ）$非常有限的数据仅在梯度流的信托窗口中也很好地工作。我们使用ADMM算法，该算法对于在某些约束下解决LASSO问题很有用。我们表明，所获得的光谱函数在有限流动时重现了输入涂片的相关函数。还讨论了几个系统和统计误差以及流动时间依赖性。
We propose the sparse modeling method to estimate the spectral function from the smeared correlation functions. We give a description of how to obtain the shear viscosity from the correlation function of the renormalized energy-momentum tensor (EMT) measured by the gradient flow method ($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.
