论文标题
具有随机初始条件的Kardar-Parisi-Zhang界面放松中的精确短时高度分布和动态相变
Exact short-time height distribution and dynamical phase transition in the relaxation of a Kardar-Parisi-Zhang interface with random initial condition
论文作者
论文摘要
我们考虑单点高度的放松（无噪声）统计数据$ h = h（x = 0，t）$，其中$ h（x，t）$是从布朗（随机）初始条件开始的一维kardar-parisi-zhang（kpz）界面的一维kardar-parisi-zhang（kpz）界面的不断发展的高度。我们发现，在短时间内，$ h $的分布采用相同的缩放表格$ - \ ln \ Mathcal {p} \ left（H，h，t \ right）= s \ left（h \ right）/\ sqrt {t} $与kpz界面驱动的h noise和我们的噪声驱动器的分布，我们找到了确切的大型大数据函数$ s（h）$ s（h）。在临界值$ h = h_c $的情况下，$ s（h）$跳跃的第二个导数，发出动态相变（DPT）。此外，我们确切地计算了导致给定$ H $的接口的最可能历史记录，并表明DPT与接口的镜子对称性$ x \ leftrightArrow -x $相关。反过来，我们发现这种对称性破坏是与$ s（h）$密切相关的大型传播函数的非凸性的结果，并描述了一个类似的问题，但在半空间中。此外，关键点$ H_C $与半空间问题的大差异功能的拐点有关。
We consider the relaxation (noise-free) statistics of the one-point height $H=h(x=0,t)$ where $h(x,t)$ is the evolving height of a one-dimensional Kardar-Parisi-Zhang (KPZ) interface, starting from a Brownian (random) initial condition. We find that, at short times, the distribution of $H$ takes the same scaling form $-\ln\mathcal{P}\left(H,t\right)=S\left(H\right)/\sqrt{t}$ as the distribution of H for the KPZ interface driven by noise, and we find the exact large-deviation function $S(H)$ analytically. At a critical value $H=H_c$, the second derivative of $S(H)$ jumps, signaling a dynamical phase transition (DPT). Furthermore, we calculate exactly the most likely history of the interface that leads to a given $H$, and show that the DPT is associated with spontaneous breaking of the mirror symmetry $x \leftrightarrow -x$ of the interface. In turn, we find that this symmetry breaking is a consequence of the non-convexity of a large-deviation function that is closely related to $S(H)$, and describes a similar problem but in half space. Moreover, the critical point $H_c$ is related to the inflection point of the large-deviation function of the half-space problem.
