Bayesian deconvolution and analysis of photoelectron or any other spectra: Fermi-liquid versus marginal Fermi-liquid behavior of the 3d electrons in Ni
Bayesian deconvolution and analysis of photoelectron or any other spectra: Fermi-liquid versus marginal Fermi-liquid behavior of the 3d electrons in Ni
复制标题
光电子或任何其他光谱的贝叶斯反卷积和分析：Ni 中 3d 电子的费米液体与边际费米液体行为
DOI：
10.1103/physrevb.58.6877
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发表时间：
1998
影响因子：
3.7
通讯作者：
S. Weiß
中科院分区：
文献类型：
--
作者：
U. Gerhardt;S. Marquardt;N. Schroeder;S. Weiß
提出了一种简单有效的实验光谱D的迭代反褶积方法。我们表明，这种“迭代贝叶斯反卷积”与更复杂的“贝叶斯分析”密切相关，也称为量化最大熵方法。在这两种情况下都需要一个真谱函数的模型m。贝叶斯分析是将实测光谱D通过各自的概率与相应的理论模型m联系起来的最有效和精确的方法，但两个严重的概念问题和两个严重的技术困难阻碍了广泛应用。我们删除这些四个障碍(我)证明分析和计算机模拟,最可能的反褶积得到作为副产品的贝叶斯分析接近真正的谱函数随着m的质量增加,(2)找到等价但更高效的优化参数包含在一个给定的模型m×之间通常的最小二乘匹配D和m的卷积前使用贝叶斯贝叶斯分析代替（iii）仅通过对n个数据点的能量求和来近似卷积，选择归一化光谱仪函数以最小化光谱两侧的误差，（iv）通过简单地重新表述n个非线性方程的相应系统来避免贝叶斯分析中经常遇到的严重收敛问题。我们还使用两种不同的物理模型，将我们的贝叶斯分析版本应用于接近费米能量约12 K的Ni（111）的正常发射的角分辨光电子能谱：与边际费米液体相比，费米液体线形状与观测到的低光子和小结合能区域的多数和少数自旋峰结构相符的可能性约为10.4倍。
We present a simple and effective iterative deconvolution of noisy experimental spectra D broadened by the spectrometer function. We show that this “iterative Bayesian deconvolution” is closely related to the more complex “Bayesian analysis,” also known as the quantified maximum-entropy method. A model m of the true spectral function is needed in both cases. The Bayesian analysis is the most powerful and precise method to relate measured spectra D to the corresponding theoretical models m via the respective probabilities, but two grave conceptual problems together with two severe technical difficulties prevented widespread application. We remove these four obstacles by (i) demonstrating analytically and also by computer simulations that the most probable deconvolution â obtained as a by-product from the Bayesian analysis gets closer to the true spectral function as the quality of m increases,(ii) finding it equivalent but vastly more efficient to optimize the parameters contained in a given model m by the usual least-squares fit between D and the convolution of m prior to the Bayesian analysis instead of using the Bayesian analysis itself for that purpose,(iii) approximating the convolution by a summation over the energies of the n data points only, with the normalization of the spectrometer function chosen to minimize the errors at both edges of the spectrum, and (iv) avoiding the severe convergence problems frequently encountered in the Bayesian analysis by a simple reformulation of the corresponding system of n nonlinear equations. We also apply our version of the Bayesian analysis to angle-resolved photoelectron spectra taken at normal emission from Ni (111) close to the Fermi energy at about 12 K, using two different physical models: Compared with the marginal Fermi liquid, the Fermi-liquid line shape turns out to be about 10 4 times more probable to conform with the observed structure of the majority and minority spin peaks in the low-photon and small-binding-energy region.