Spectral function of hadrons on finite temperature lattice QCD

有限温度下强子的谱函数具有丰富的物理内容，即有限温度环境下强子的质量和束缚态。最近，一些作者试图从晶格QCD模拟计算的传播子中确定谱函数。该问题属于线性方程的逆问题，但它具有病态性质，难以求逆。利用截断奇异值分解和最大熵法，提出了一种新的谱函数正则化方案。我们的方法总是给出一个满足谱函数正性要求的解。我们将该方法应用于时间点阵大小Nt=20的点阵数据，并分析了伪标量和矢量通道。在我们的晶格中，Nt=20对应于QCD相变之前的温度。熵有几种定义。我们尝试了两种定义，结果一致。本分析所用的数据是在淬火近似下得到的，不包含动态费米子效应。由于晶格上费米子的加倍问题，处理费米子是困难的。我们开发了一种新的晶格费米子算法，它比标准费米子具有更少的种。并对该方法进行了可行性研究。本项目介绍了一个数据分析系统。利用该系统，我们还模拟了Nelson量子随机过程，并估计了电子通过磁性薄膜的隧穿时间。

The spectral function of hadrons at finite temperature is expected to have rich physical contents, i.e., its mass and bound state under environment at finite temperature. Recently several authors have tried to determine the spectral function from propagators calculated by lattice QCD simulations. The problem is classified to an inverse problem of a linear equation, but it has ill-posed nature and hard to invert. We developed a new regularization scheme to find a spectral function by the use of truncated singular value decomposition and maximal entropy method. Our method always give a solution which satisfies the positivity requirement for the spectral function. We applied the method to lattice date with temporal lattice size Nt=20 and analyzed pseudo scalar and vector channels. On our lattice, Nt=20 corresponds to temperature just before the QCD phase transition. There are several definitions of entropy. We tried two definitions and the results are consistent.The data used in this analysis are made under quenched approximation and do not contain dynamical fermion effects. The treatment of fermions on the lattice is difficult because of its doubling problem. We developed a new algorithm for the lattice fermion which has less species than the standard fermion. We also made the feasibility study of the method.A system for the data analysis was introduced in this project. By the use of the system, we also made simulations of Nelson's quantum stochastic process and estimated tunneling time of the electron through magnetic thin films.