Smith Naftali R
Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, Israel.
Phys Rev E. 2022 Oct;106(4-1):044111. doi: 10.1103/PhysRevE.106.044111.
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 -lnP(H,t)=S(H)/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↔-x of the interface. In turn, we find that this symmetry breaking is a consequence of the nonconvexity 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.
我们考虑单点高度(H = h(x = 0,t))的弛豫（无噪声）统计量，其中(h(x,t))是一维 Kardar - Parisi - Zhang（KPZ）界面的演化高度，初始条件为布朗（随机）初始条件。我们发现，在短时间内，(H)的分布与由噪声驱动的 KPZ 界面的(H)分布具有相同的标度形式(-\ln P(H,t)=S(H)/\sqrt{t})，并且我们通过解析方法求出了精确的大偏差函数(S(H))。在临界值(H = H_{c})处，(S(H))的二阶导数发生跃变，这标志着一个动力学相变（DPT）。此外，我们精确计算了导致给定(H)的界面的最可能历史，并表明 DPT 与界面的镜像对称(x↔ - x)的自发破缺相关。反过来，我们发现这种对称破缺是一个与(S(H))密切相关的大偏差函数非凸性的结果，该大偏差函数描述了一个类似但在半空间中的问题。此外，临界点(H_{c})与半空间问题的大偏差函数的拐点有关。
