带随机初始条件的随机梅洛尼克（melonic）动力学
Stochastic melonic kinetics with random initial conditions
AI总结：
该研究采用朗之万型方程的随机视角，利用大N极限下张量不变量的自平均性质，研究随机复张量场相序动力学的低温行为，给出转变温度公式并辅以数值模拟，开辟相关新研究方向。
摘要：
与随机张量或张量场论相关的概率律传统上是平衡分布。本文采用随机视角，通过一类朗之万（Langevin）型方程来实现量子化。我们重点研究了D维空间中、尺寸为N且秩为d的随机复张量场$T_{i_1\textbf{…}i_d}(x,t)$的相序动力学的低温行为。我们提出的方法利用了大N极限下张量不变量的自平均性质。在该区域中，动力学由梅洛尼克（melonic）扇区主导，我们在淬火极限下研究其行为——在该极限下，涉及d-1个指标的缩聚会在与单位矩阵成正比的对角矩阵附近发生自平均。本工作尤其聚焦于循环（即非分支）梅洛尼克扇区，研究系统回归平衡态的方式与温度以及势函数形状的关联。我们特别给出了这些区域之间转变温度的通用公式。论文还辅以数值模拟以支撑理论分析，其核心目的是为这一新的研究领域开辟方向。
英文摘要：
The probability laws associated with random tensors or tensor field theories are traditionally equilibrium distributions. In this paper, we consider a stochastic point of view, and approach the quantization by a Langevin type equation. We especially address the low-temperature behavior of the phase ordering kinetics of a stochastic complex tensor field $T_{i_1\cdots i_d}(x,t)$ of size $N$ and rank $d$ in dimension $D$. The method we propose use the self averaging property of the tensorial invariants in the large $N$ limit. In this regime, the dynamics is governed by the melonic sector, whose behavior is studied in the quenched limit, where the contractions involving $d-1$ indices self-average around a diagonal matrix proportional to the identity. The following work especially focuses on the cyclic (i.e. non-branching) melonic sector, and we study the way that the system returns to the equilibrium regime regarding the temperature and the shape of the potential. In particular, we provide a general formula for the transition temperature between these regimes. The manuscript is accompanied by numerical simulations to support the theoretical analysis, and essentially aims to open towards this new field of investigation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
