Bayesian approach to spectral function reconstruction for Euclidean quantum field theories.
Bayesian approach to spectral function reconstruction for Euclidean quantum field theories.
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DOI：
10.1103/physrevlett.111.182003
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发表时间：
2013-07
影响因子：
8.6
通讯作者：
Y. Burnier;A. Rothkopf
中科院分区：
文献类型：
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作者：
Y. Burnier;A. Rothkopf
我们提出了一种从欧几里德时间相关器数据推断谱函数的新颖方法，该方法与现代贝叶斯概念密切相关。我们的方法与最大熵方法（MEM）有很大不同。针对先验概率假设了一组新的公理，从而改进了表达式，该表达式没有 Shanon-Jaynes 熵中存在的渐近平坦方向。超参数被明确地积分出来，将我们从最大熵方法的证据方法背后的高斯近似中解放出来。我们在重夸克势的非微扰提取的背景下对我们的方法进行了现实测试。基于硬热环相关器模拟数据，我们对数据点的数量及其准确性提出了严格的要求，以成功从晶格 QCD 中提取电势。最后，我们重新研究了先前研究中的淬火晶格 QCD 相关器，并提供了 T=2.33T(C) 时改进的电势估计。
We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33T(C).