Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface

各向同性自旋链中 KPZ 标度的非线性涨落流体力学

Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains

本文提出一种非线性涨落流体力学理论，通过耦合局部自旋磁化强度及其有效速度两个随机模式，解释了可积各向同性自旋链中反常自旋动力学的出现，预测了 KPZ 标度下的准高斯对称涨落分布。

各向同性自旋链中 Kardar-Parisi-Zhang 普适类的部分但确定的涌现

Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains

本文结合数值模拟与 KPZ 普适类精确研究框架，证实可积各向同性自旋链中两点量符合 KPZ 标度律，确立了 KPZ 类的部分涌现，并发现能量流下该标度律在 Galilean 变换中保持不变。

PDE estimates for multi-dimensional KPZ equation

We study in this series of articles the Kardar-Parisi-Zhang (KPZ) equation $$ \partial_t h(t,x)=νΔh(t,x)+λV(|\nabla h(t,x)|) +\sqrt{D}\, η(t,x), \qquad x\in{\mathbb{R}}^d $$ in $d\ge 1$ dimensions. The forcing term $η$ in the right-hand side is a regularized white noise. The deposition rate $V$ is assumed to be isotropic and convex. Assuming $V(0)\ge 0$, one finds $V(|\nabla h|)\ltimes |\nabla h|^2$ for small gradients, yielding the equation which is most commonly used in the literature. The present article is dedicated to existence results and PDE estimates for the solution. Our results exten…

Kardar-Parisi-Zhang和二维安德森局域化中的玻璃性质：本征态和波包

Kardar-Parisi-Zhang and glassy properties in 2D Anderson localization: eigenstates and wave packets

本文通过KPZ框架揭示二维安德森局域化中波动的普遍性及玻璃性质，展示本征态与波包的标度行为。

Classification of (2+1)-Dimensional Growing Surfaces Using Schramm-Loewner Evolution

Statistical behavior and scaling properties of iso-height lines in three different saturated two-dimensional grown surfaces with controversial universality classes are investigated using ideas from Schramm-Loewner evolution (SLE$_κ$). We present some evidence that the iso-height lines in the ballistic deposition (BD), Eden and restricted solid-on-solid (RSOS) models have conformally invariant properties all in the same universality class as the self-avoiding random walk (SAW), equivalently SLE$_{8/3}$. This leads to the conclusion that all these discrete growth models fall into the same univer…

二维主动标量湍流中节线的拓扑与共形不变性

Topology and the Conformal Invariance of Nodal Lines in Two-Dimensional Active Scalar Turbulence

本文针对二维主动标量湍流逆级联中节点等值线的 SLE 与共形不变性，提出通量畴壁、拓扑绕数和 Clebsch 标量有效理论，并以 Liouville CFT 解释其普适机制。