卡尔达-帕里西-张普适类与锚定图姆界面。

Kardar-Parisi-Zhang universality class and the anchored Toom interface.

作者信息

Barkema G T, Ferrari P L, Lebowitz J L, Spohn H

机构信息

Institute for Theoretical Physics, Universiteit Utrecht, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands and Instituut-Lorentz, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands.

Institute for Applied Mathematics, Bonn University, Endenicher Allee 60, 53115 Bonn, Germany.

出版信息

Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042116. doi: 10.1103/PhysRevE.90.042116. Epub 2014 Oct 8.

DOI:10.1103/PhysRevE.90.042116

PMID:25375447

Abstract

We revisit the anchored Toom interface and use Kardar-Parisi-Zhang scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. The predictions, which contain no free parameter, are numerically well confirmed for space-time statistics in the stationary state. In particular, the spatial fluctuations of the interface computed numerically agree well with those given by the GOE edge distribution of Tracy and Widom [Commun. Math. Phys. 177, 727 (1996)].

摘要

我们重新审视锚定的图姆界面，并运用卡达尔-帕里西-张标度理论来论证界面涨落由艾里1过程所支配，其中空间和时间的作用相互交换。这些不含自由参数的预测，在稳态下的时空统计方面得到了数值上的很好验证。特别是，通过数值计算得到的界面空间涨落与特雷西和威多姆的高斯正交系综边缘分布[《数学物理通讯》177, 727 (1996)]所给出的结果吻合得很好。