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Spectral function of hadrons on finite temperature lattice QCD

有限温度晶格 QCD 上的强子谱函数

基本信息

批准号：
11640268
负责人：
HASHIMOTO Takaaki
金额：
$ 2.18万
依托单位：
Fukui University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640268/
关键词：
QCD lattice gauge theory hadron spectral function finite temperature field theory quantum stochastic process tunneling time

项目摘要

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.

有限温度下强子的谱函数具有丰富的物理内容，在有限温度环境下的质量和束缚态。最近，一些作者试图从格点QCD模拟计算的传播子中确定谱函数。该问题被归结为一个线性方程的反问题，但它具有不适定性和难以反演。利用截断奇异值分解和极大熵方法，提出了一种新的正则化方法。我们的方法总是给出一个解决方案，满足正性要求的谱函数。我们将该方法应用于时间网格大小Nt=20的网格数据，并分析了伪标量和矢量通道。在我们的晶格上，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，结果是一致的，分析中所用的数据是在猝灭近似下得到的，不包含动力学费米子效应。费米子在晶格上的处理是困难的，因为它的加倍问题。我们发展了一种新的计算格点费米子的算法，格点费米子的种类比标准费米子少。并对该方法的可行性进行了研究，介绍了一个数据分析系统。利用该系统对纳尔逊量子随机过程进行了模拟，并估算了电子在磁性薄膜中的隧穿时间。