论文标题
大N扩展和弦理论中的Keldysh旋转从平衡中
Keldysh Rotation in the Large-N Expansion and String Theory Out of Equilibrium
论文作者
论文摘要
我们扩展了对具有矩阵自由度$ m $的一般非平衡多体系统扩展的研究，其双重描述是双字符串理论中表面拓扑的总和，降至schwinger-keldysh的形式主义的Keldysh旋转版本。 Keldysh旋转交易原始字段$ M_ \ pm $ - 定义为封闭时间轮廓的前部和向后段的$ m $的值 - 对于它们的线性组合$ M _ {\ textrm {cl}}} $和$ m _ {\ textrm {qu}} $，n.ptastical和calteral''首先，我们为Keldysh旋转形式的非平衡Feynman图开发了一种新颖的“路标”符号，这大大简化了分析。在Keldys旋转之前，发现双字符串理论扩展中的每个世界表面$σ$都在$σ^\ pm $中表现出三重分解，对应于封闭时间轮廓的向前和向后段，以及$σ^\ wedge $，$σ^\ wedge $，与两个细分市场相遇的瞬间相对应。在旋转Keldysh之后，我们发现双字符串理论的世界表面表面$σ$经历了一个非常不同的自然分解：$σ$由“经典”部分$σ^{\ textrm {cl}} $组成，和“量子上点缀”部分$σ^^^{\ textrm {qu}} $。我们表明，$σ$的两个部分都带有自己的独立属扩展。在世界表拓扑上的非平衡总和自然被完善成一和分成每个$σ$的双重分解为其经典和量子部分。我们将此图片应用于量子非平衡系统的经典限制（与热浴有或不相互作用），并发现在这些限制中，双弦扰动理论的扩展将其缩小到其适当定义的经典限制。
We extend our study of the large-$N$ expansion of general non-equilibrium many-body systems with matrix degrees of freedom $M$, and its dual description as a sum over surface topologies in a dual string theory, to the Keldysh-rotated version of the Schwinger-Keldysh formalism. The Keldysh rotation trades the original fields $M_\pm$ -- defined as the values of $M$ on the forward and backward segments of the closed time contour -- for their linear combinations $M_{\textrm{cl}}$ and $M_{\textrm{qu}}$, known as the "classical" and "quantum" fields. First we develop a novel "signpost" notation for non-equilibrium Feynman diagrams in the Keldysh-rotated form, which simplifies the analysis considerably. Before the Keldysh rotation, each worldsheet surface $Σ$ in the dual string theory expansion was found to exhibit a triple decomposition into the parts $Σ^\pm$ corresponding to the forward and backward segments of the closed time contour, and $Σ^\wedge$ which corresponds to the instant in time where the two segments meet. After the Keldysh rotation, we find that the worldsheet surface $Σ$ of the dual string theory undergoes a very different natural decomposition: $Σ$ consists of a "classical" part $Σ^{\textrm{cl}}$, and a "quantum embellishment" part $Σ^{\textrm{qu}}$. We show that both parts of $Σ$ carry their own independent genus expansion. The non-equilibrium sum over worldsheet topologies is naturally refined into a sum over the double decomposition of each $Σ$ into its classical and quantum part. We apply this picture to the classical limits of the quantum non-equilibrium system (with or without interactions with a thermal bath), and find that in these limits, the dual string perturbation theory expansion reduces to its appropriately defined classical limit.
