热介质中的非马尔可夫重夸克平衡与平衡关联函数
Non-Markovian heavy-quark equilibration and equilibrium correlation function in a thermal medium
AI总结：
研究热介质中非马尔可夫重夸克平衡与关联函数，在朗之万框架内计算粲夸克流-流关联函数，用格林-久保公式提取扩散系数，扩展形式考虑记忆效应，比较不同方程解，发现记忆效应影响瞬态结构但不改变输运系数值。
AI中文摘要：
我们在朗之万框架内计算了粲夸克流-流关联函数，并使用格林-久保公式提取了重夸克扩散系数。通过包含指数衰减记忆核的广义朗之万方程进一步扩展形式以评估关联函数。发现记忆效应定性地改变了电流关联的瞬态结构，但在非相对论极限下输运系数值不变。此外，研究了有记忆时的重夸克热化，比较了广义福克-普朗克方程的非平衡解与广义朗之万方程在非相对论极限下的解。还考虑了关联噪声情况的相对论版本，观察到记忆效应可导致重夸克在非马尔可夫浴中出现阻尼振荡平衡。
英文摘要：
We compute the charm-quark current-current correlation function within the Langevin framework and extract the heavy-quark diffusion coefficient using the Green--Kubo formula. The formalism is further extended to evaluate the correlation function using a generalized Langevin equation that incorporates memory effects via an exponentially decaying memory kernel. We find that while memory effects qualitatively modify the transient structure of the current correlations, the value of the transport coefficient remains unchanged in the non-relativistic limit. In addition, we investigate heavy-quark thermalization in the presence of memory and compare the non-equilibrium solution of a generalized Fokker--Planck equation with the one obtained from the generalized Langevin equation in the non-relativistic limit. We also consider the relativistic version of the correlated noise case and observe that memory effects can give rise to a damped, oscillatory equilibration of the heavy quark in a non-Markovian bath.
