Classical model for diffusion and thermalization of heavy quarks in a hot medium: memory and out-of-equilibrium effects
Classical model for diffusion and thermalization of heavy quarks in a hot medium: memory and out-of-equilibrium effects
复制标题
热介质中重夸克扩散和热化的经典模型：记忆和不平衡效应
DOI：
10.1088/1674-1137/43/9/094105
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Das Santosh Kumar
中科院分区：
文献类型：
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作者：
Ruggieri Marco;Frasca Marco;Das Santosh Kumar
我们考虑了一个简单的重夸克在热浴中扩散的模型，用一组振子系综来模拟热浴中重夸克的扩散，这些振子按照热分布或具有饱和尺度的非平衡分布分布。在这个模型中，很容易通过改变振子的分布来引入记忆效应：我们通过引入高斯分布dN/dω来对它们进行建模，该分布可以从δ函数连续变形，从而给出马尔可夫耗散，从而给出一个具有记忆的广义核。通过推导重夸克在浴池中的运动方程，我们讨论了耗散是如何作为振子对浴池的反向反应而自然产生的。此外，该方程的精确解允许将热化时间定义为消除对初始条件的任何记忆所需的时间。我们发现，在保持耦合不变的情况下，耗散核的加宽降低了热化时间。我们还导出了水槽的涨落耗散定理，并用它估计了重夸克的动量扩散主导漂移的运动学机制。我们发现，当K_0/E较小时，扩散更为重要，其中K_0和E分别表示重夸克的初始能量和水槽的平均能量。
We consider a simple model for the diffusion of heavy quarks in a hot bath, modeling the latter by an ensemble of oscillators distributed according to either a thermal distribution or to an out-of-equilibrium distribution with a saturation scale. In this model it is easy to introduce memory effects by changing the distribution of oscillators: we model them by introducing a Gaussian distribution, dN/dω, which can be deformed continuously from a δ-function, giving a Markov dissipation, to a broad kernel with memory. Deriving the equation of motion of the heavy quark in the bath, we remark how dissipation comes out naturally as an effect of the back-reaction of the oscillators on the bath. Moreover, the exact solution of this equation allows to define the thermalization time as the time necessary to remove any memory of the initial conditions. We find that the broadening of the dissipative kernel, while keeping the coupling fixed, lowers the thermalization time. We also derive the fluctuation-dissipation theorem for the bath, and use it to estimate the kinematic regime in which momentum diffusion of the heavy quark dominates over drift. We find that diffusion is more important as long as K_0/E is small, where K_0 and E denote the initial energy of the heavy quark and the average energy of the bath, respectively.