Stationary Correlations for the 1D KPZ Equation

被引：70

作者：

Imamura, Takashi ^{[1
]}

Sasamoto, Tomohiro ^{[2
,3
]}

机构：

[1] Univ Tokyo, Res Ctr Adv Sci & Technol, Tokyo, Japan

[2] Chiba Univ, Dept Math & Informat, Chiba, Japan

[3] Tech Univ Munich, Zentrum Math, Garching, Germany

来源：

JOURNAL OF STATISTICAL PHYSICS | 2013年 / 150卷 / 05期

关键词：

KPZ equation; Replica method; Exact solution; Fredholm determinant; POLYNUCLEAR GROWTH-MODEL; UNIVERSAL FLUCTUATIONS; SCALING FUNCTIONS; BETHE-ANSATZ; FREE-ENERGY; DISTRIBUTIONS; INTERFACES; SURFACE; POLYMER; TASEP;

D O I：

10.1007/s10955-013-0710-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable. Developing techniques for dealing with this initial condition in the replica analysis, we elucidate some exact nature of the height fluctuation for the KPZ equation. In particular, we obtain an explicit representation of the probability distribution of the height in terms of the Fredholm determinants. Furthermore from this expression, we also get the exact expression of the space-time two-point correlation function.

引用

页码：908 / 939

页数：32

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