有限记忆扩散中的累积量动力学
Cumulant dynamics in finite-memory diffusion
AI总结：
本文通过推广Fick扩散到Maxwell-Cattaneo扩散，研究了有限电流弛豫时间对QCD临界点附近守恒荷涨落累积量的影响，发现电流记忆效应会抑制、移动和重塑累积量的非单调行为。
摘要：
守恒荷的涨落是量子色动力学(QCD)临界点的主要提议信号之一，但它们的解释需要对夸克-胶子等离子体(QGP)火球有限寿命期间涨落关联子如何演化进行动力学描述。这种演化的标准基线是Fick扩散，其中扩散流瞬时跟随局域密度梯度。当电流弛豫时间变得与相关涨落模式的弛豫时间相当时，这种瞬时电流极限可能会错过延迟响应效应。在这项工作中，我们将这一基线扩展到Maxwell-Cattaneo扩散，其中电流在有限时间尺度上弛豫，因此保留记忆。我们推导了多点Wigner函数的封闭演化方程，并将冻结关联子转换为沿QCD相图中代表性轨迹的接受度依赖累积量。虽然Fick扩散已经导致关联子滞后于其瞬时平衡值，但有限电流弛豫引入了超出这种扩散滞后的额外记忆效应。因此，相对于瞬时平衡和Fick扩散，电流记忆可以抑制、移动和重塑累积量的非单调行为，其中最高阶累积量及其比率中的效应最为明显。
英文摘要：
Fluctuations of conserved charges are among the main proposed signatures of the quantum chromodynamics (QCD) critical point, but their interpretation requires a dynamical description of how fluctuation correlators evolve during the finite lifetime of the quark--gluon plasma (QGP) fireball. The standard baseline for this evolution is Fickian diffusion, in which the diffusive current follows the local density gradient instantaneously. This instantaneous-current limit can miss delayed-response effects when the current-relaxation time becomes comparable to the relaxation time of the relevant fluctuation modes. In this work we extend this baseline to Maxwell--Cattaneo diffusion, where the current relaxes on a finite time scale and therefore retains memory. We derive closed evolution equations for multi-point Wigner functions and convert the freezeout correlators into acceptance-dependent cumulants along representative trajectories in the QCD phase diagram. While Fickian diffusion already causes the correlators to lag behind their instantaneous equilibrium values, finite current relaxation introduces an additional memory effect beyond this diffusive lag. As a result, current memory can suppress, shift, and reshape the non-monotonic behavior of the cumulants relative to both instantaneous equilibrium and Fickian diffusion, with the most visible effects appearing in higher-order cumulants and their ratios.
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