Halpin-Healy Timothy, Lin Yuexia
Physics Department, Barnard College, Columbia University, New York, New York 10027, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):010103. doi: 10.1103/PhysRevE.89.010103. Epub 2014 Jan 16.
Motivated by the recent exact solution of the stationary-state Kardar-Parisi-Zhang (KPZ) statistics by Imamura and Sasamoto [ Phys. Rev. Lett. 108 190603 (2012)], as well as a precursor experimental signature unearthed by Takeuchi [ Phys. Rev. Lett. 110 210604 (2013)], we establish here the universality of these phenomena, examining scaling behaviors of directed polymers in a random medium, the stochastic heat equation with multiplicative noise, and kinetically roughened KPZ growth models. We emphasize the value of cross KPZ-class universalities, revealing crossover effects of experimental relevance. Finally, we illustrate the great utility of KPZ scaling theory by an optimized numerical analysis of the Ulam problem of random permutations.
受今村和笹本近期对稳态 Kardar-Parisi-Zhang（KPZ）统计量的精确解[《物理评论快报》108 190603（2012）]以及竹内发现的一个先兆实验特征[《物理评论快报》110 210604（2013）]的启发，我们在此确立这些现象的普遍性，研究随机介质中定向聚合物、具有乘性噪声的随机热方程以及动力学粗糙化的 KPZ 增长模型的标度行为。我们强调跨 KPZ 类普遍性的价值，揭示具有实验相关性的交叉效应。最后，我们通过对随机排列的乌拉姆问题进行优化数值分析来说明 KPZ 标度理论的巨大效用。
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