Fogedby H C
Institute of Physics and Astronomy, University of Aarhus, DK-8000, Aarhus C, Denmark.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt A):5065-80. doi: 10.1103/physreve.59.5065.
We present a canonical phase-space approach to stochastic systems described by Langevin equations driven by white noise. Mapping the associated Fokker-Planck equation to a Hamilton-Jacobi equation in the nonperturbative weak noise limit we invoke a principle of least action for the determination of the probability distributions. We apply the scheme to the noisy Burgers and Kardar-Parisi-Zhang equations and discuss the time-dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the symmetric stationary Gaussian distribution. In the short-time region we discuss heuristically the nonlinear soliton contributions and derive an expression for the distribution in accordance with the directed polymer-replica and asymmetric exclusion model results. We also comment on the distribution in higher dimensions.
我们提出了一种规范的相空间方法，用于处理由白噪声驱动的朗之万方程所描述的随机系统。在非微扰弱噪声极限下，将相关的福克 - 普朗克方程映射为哈密顿 - 雅可比方程，我们引入最小作用量原理来确定概率分布。我们将该方案应用于有噪声的伯格斯方程和卡达尔 - 帕里西 - 张方程，并讨论了随时间变化的概率分布和平稳概率分布。在一维情况下，我们推导出了趋近于对称平稳高斯分布的长时间倾斜分布。在短时间区域，我们试探性地讨论了非线性孤子的贡献，并根据定向聚合物 - 副本和非对称排斥模型的结果推导出了分布的表达式。我们还对高维情况下的分布进行了评论。
