Time-averaged height distribution of the Kardar–Parisi–Zhang interface
Time-averaged height distribution of the Kardar–Parisi–Zhang interface
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DOI：
10.1088/1742-5468/ab16c1
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发表时间：
2019-02
期刊：
影响因子：
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通讯作者：
Naftali R. Smith;B. Meerson;A. Vilenkin
中科院分区：
文献类型：
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作者：
Naftali R. Smith;B. Meerson;A. Vilenkin
本文研究了1 + 1维Kardar-Parisi-Zhang（KPZ）界面在x = 0点时均高度的全概率分布。我们专注于短时间和平坦的初始条件，并采用最佳波动方法来确定的方差和第三累积量的分布，以及非对称拉伸指数尾部。尾部按和缩放，类似于指定时间的单点KPZ高度统计量的先前确定的尾部。最佳界面的历史，主导这些尾巴，是显着不同的。值得注意的是，在x = 0时界面高度的最佳历史是时间的非单调函数：在中间时间达到最大（或最小）界面高度。我们还解决了一个更一般的问题，确定观察一个给定的高度历史的KPZ接口在点x = 0的概率密度。
We study the complete probability distribution of the time-averaged height at point x = 0 of an evolving 1 + 1 dimensional Kardar–Parisi–Zhang (KPZ) interface . We focus on short times and flat initial condition and employ the optimal fluctuation method to determine the variance and the third cumulant of the distribution, as well as the asymmetric stretched-exponential tails. The tails scale as and , similarly to the previously determined tails of the one-point KPZ height statistics at specified time . The optimal interface histories, dominating these tails, are markedly different. Remarkably, the optimal history, , of the interface height at x = 0 is a non-monotonic function of time: the maximum (or minimum) interface height is achieved at an intermediate time. We also address a more general problem of determining the probability density of observing a given height history of the KPZ interface at point x = 0.