论文标题
Jimwlk进化，Lindblad方程和量子古典对应关系
JIMWLK Evolution, Lindblad Equation and Quantum-Classical Correspondence
论文作者
论文摘要
在彩色玻璃冷凝物（CGC）有效理论中，具有较大纵向动量的价值的物理学反映在横向平面中颜色电荷的分布中。通过与某些准概率权重功能性$ W [{\ Mathbf {J}}] $在经典的颜色电荷上整合的平均自由度的平均值是通过jimwlk方程控制的。在本文中，我们根据降低的硬gluons的密度矩阵$ \hatρ$控制的有效量子场理论对这种设置进行了重新制定，而硬glu子则是在正确整合软gluon“环境”后获得的。我们表明，该密度矩阵的演变在致密和稀限的速度中具有lindblad方程的形式。准概率分布（重量）功能$ W $通过对Wigner-Weyl-Weyl量子 - 古典通信的概括而与降低的密度矩阵$ \hatρ$直接相关，该通讯根据相位空间上的经典动力学来重新制定希尔伯特空间上的量子动力学。在目前的情况下，相位空间是非abelian的，并且由横向颜色电荷密度$ {\ mathbf {j}} $的组件跨越。相同的信件将$ \hatρ$的lindblad方程式映射到$ w $的jimwlk进化方程中。
In the Color Glass Condensate(CGC) effective theory, the physics of valence gluons with large longitudinal momentum is reflected in the distribution of color charges in the transverse plane. Averaging over the valence degrees of freedom is effected by integrating over classical color charges with some quasi probability weight functional $W[{\mathbf{j}}]$ whose evolution with rapidity is governed by the JIMWLK equation. In this paper, we reformulate this setup in terms of effective quantum field theory on valence Hilbert space governed by the reduced density matrix $\hatρ$ for hard gluons, which is obtained after properly integrating out the soft gluon "environment". We show that the evolution of this density matrix with rapidity in the dense and dilute limits has the form of Lindblad equation. The quasi probability distribution (weight) functional $W$ is directly related to the reduced density matrix $\hatρ$ through the generalization of the Wigner-Weyl quantum-classical correspondence, which reformulates quantum dynamics on Hilbert space in terms of classical dynamics on the phase space. In the present case the phase space is non Abelian and is spanned by the components of transverse color charge density ${\mathbf{j}}$. The same correspondence maps the Lindblad equation for $\hatρ$ into the JIMWLK evolution equation for $W$ .
