Slow decorrelations in Kardar–Parisi–Zhang growth
Slow decorrelations in Kardar–Parisi–Zhang growth
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Kardar-Parisi-Zhang 增长的缓慢去相关性
DOI：
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发表时间：
2008
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通讯作者：
P. Ferrari
中科院分区：
文献类型：
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作者：
P. Ferrari
对于Kardar-Parisi-Zhang（KPZ）类的1+1维随机增长模型，波动在时间t内以t1/3的形式增长，在固定时间尺度上的相关长度为t2/3.在这项工作中，我们讨论的时间相关性的规模。对于KPZ类的一个代表，多核增长模型，我们表明，时空是非平凡的纤维，具有慢的方向与解相关指数等于1，而不是通常的2/3。这些方向是与表面斜率相关的偏微分方程的特征曲线。因此，以前证明的类空路径的结果将适用于整个时空，除了沿着慢曲线。
For stochastic growth models in the Kardar–Parisi–Zhang (KPZ) class in 1+1 dimensions, fluctuations grow as t1/3 during time t and the correlation length at a fixed time scales as t2/3. In this work we discuss the scale of time correlations. For a representative of the KPZ class, the polynuclear growth model, we show that the space–time is non-trivially fibered, having slow directions with decorrelation exponent equal to 1 instead of the usual 2/3. These directions are the characteristic curves of the partial differential equation associated with the surface’s slope. As a consequence, previously proven results for space-like paths will hold for the whole space–time except along the slow curves.