Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Department of Physics, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Phys Rev E. 2018 Apr;97(4-1):042130. doi: 10.1103/PhysRevE.97.042130.
We study the short-time distribution P(H,L,t) of the two-point two-time height difference H=h(L,t)-h(0,0) of a stationary Kardar-Parisi-Zhang interface in 1+1 dimension. Employing the optimal-fluctuation method, we develop an effective Landau theory for the second-order dynamical phase transition found previously for L=0 at a critical value H=H_{c}. We show that |H| and L play the roles of inverse temperature and external magnetic field, respectively. In particular, we find a first-order dynamical phase transition when L changes sign, at supercritical H. We also determine analytically P(H,L,t) in several limits away from the second-order transition. Typical fluctuations of H are Gaussian, but the distribution tails are highly asymmetric. The tails -lnP∼|H|^{3/2}/sqrt[t] and -lnP∼|H|^{5/2}/sqrt[t], previously found for L=0, are enhanced for L≠0. At very large |L| the whole height-difference distribution P(H,L,t) is time-independent and Gaussian in H, -lnP∼|H|^{2}/|L|, describing the probability of creating a ramplike height profile at t=0.
我们研究了一维静止 Kardar-Parisi-Zhang 界面的两点两时高度差 H=h(L,t)-h(0,0)的短时分布 P(H,L,t)。通过最优涨落方法，我们为之前在 L=0 处临界值 H=H_{c}处发现的二阶动力学相变发展了一种有效的朗道理论。我们表明，|H|和 L 分别扮演着逆温度和外磁场的角色。特别是，我们在超临界 H 时发现了当 L 改变符号时存在一级动力学相变。我们还在远离二阶相变的几个极限下解析地确定了 P(H,L,t)。H 的典型涨落是高斯的，但分布尾部是高度不对称的。对于 L=0 之前发现的 -lnP∼|H|^{3/2}/sqrt[t]和 -lnP∼|H|^{5/2}/sqrt[t]尾部，对于 L≠0 会增强。在非常大的 |L|时，整个高度差分布 P(H,L,t)在 H 中是时间独立的和高斯的，-lnP∼|H|^{2}/|L|，描述了在 t=0 时创建类似 ramp 的高度分布的概率。
