Dynamical Structure of the Quark-Gluon Plasma based on Lattice QCD with Bayesian Statistics

在夸克胶子等离子体内部，由于热德拜屏蔽，夸克反夸克势变弱。结果，由重夸克组成的束缚态在一定的临界温度以上熔化。然而，熔化温度和限制-退禁闭相变的临界温度之间的精确关系。我们进行了晶格QCD模拟来回答这个问题，发现像J/Psi这样的重碳原子甚至可以存活到临界温度的1.7倍。大体积模拟以及贝叶斯统计的使用在这项研究中起着至关重要的作用。在中子星和夸克星内部，可能存在由去禁闭夸克组成的夸克物质。由于在费米面上夸克-夸克相互作用总是存在一个吸引人的通道，夸克物质处于色超导状态。我们对色超导态与正常态之间的相变进行了Ginzburg-Landau分析，发现由于胶子的热涨落，相变被驱动到一级。我们用最大熵方法分析了在晶格上计算的激发重子谱。结果表明，该方法可以准确地提取出核子正、负激发态的位置。此外，由于格子的离散化，该方法具有足够的能力来分离物理光谱和非物理光谱。

Inside the quark-gluon plasma, the quark-anti-quark potential becomes weak due to the thermal Debye screening. As a result, the bound states composed of heavy-quarks melt down above certain critical temperature. However, the precise relation between the melting temperature and the critical temperature of the confinement-deconfinement phase transition.We have carried out lattice QCD simulations to answer this problem and have found that heavy charmonium such as J/Psi can survive even up to 1.7 times the critical temperature. The large volume simulations as well as the use of the Bayesian statistics play essential role in this study.In the interior of the neutron stars and quark stars, there may exist quark matter composed of deconfined quarks. Since there is always an attractive channel in the quark-quark interaction at the Fermi surface, quark matter is in the color superconducting state.We have carried our Ginzburg-Landau analysis of the phase transition between the color superconducting state and the normal state and found that the phase transition is driven to first order due to the thermal fluctuation of the gluons.We have applied the maximum entropy method to analyses the excited baryon spectra calculated on the lattice. It was found that the method can extract the position of the positive and negative excited states of the nucleon correctly. Also, the method is powerful enough to separate the physical spectra and the unphysical spectra due to lattice discretization.