论文标题
耦合kPz方程从相互作用的扩散中衍生而来
Derivation of coupled KPZ equations from interacting diffusions driven by a single-site potential
论文作者
论文摘要
Kardar-Parisi-Zhang（KPZ）方程是一种随机部分微分方程，它源自各种显微镜模型，并且建立了一种强大的方法来得出KPZ方程的方法是数学和物理学中的基本问题。作为微观模型，我们考虑了多物种相互作用的扩散过程，其动力学是由满足某些规律性条件的非线性电势驱动的。特别是，我们研究了与平衡下高温状态相关的波动场的渐近行为。作为主要结果，我们表明，当每个物种的特征速度相同时，在移动框架中看到的波动场的家族以这种速度收敛到耦合的KPZ方程。我们的方法基于泰勒的扩展参数，该论点将谐波电位作为主要部分提取。该论点在不假设特定形式的电势的情况下起作用，从而以强大的方式得出了耦合的kPz方程。
The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to establish a robust way to derive the KPZ equation is a fundamental problem both in mathematics and in physics. As a microscopic model, we consider multi-species interacting diffusion processes, whose dynamics is driven by a nonlinear potential which satisfies some regularity conditions. In particular, we study asymptotic behavior of fluctuation fields associated with the processes in the high temperature regime under equilibrium. As a main result, we show that when the characteristic speed of each species is the same, the family of the fluctuation fields seen in moving frame with this speed converges to the coupled KPZ equations. Our approach is based on a Taylor expansion argument which extracts the harmonic potential as a main part. This argument works without assuming a specific form of the potential and thereby the coupled KPZ equations are derived in a robust way.
