论文标题
从宏观波动理论到kardar-parisi-zhang方程的跨界控制控制了超出爱因斯坦扩散之外的大偏差
The crossover from the Macroscopic Fluctuation Theory to the Kardar-Parisi-Zhang equation controls the large deviations beyond Einstein's diffusion
论文作者
论文摘要
我们研究了宏观波动理论（MFT）的交叉，该理论描述了后期1D随机扩散系统，再到较早描述Kardar-Parisi-Zhang（KPZ）方程的弱噪声理论（WNT）。我们专注于在时间依赖性随机场中扩散的示例，在诱发不对称性的非典型方向上观察到。交叉由非线性系统描述，该系统在假想时间内在衍生物和标准的非线性Schrodinger方程之间进行了插值。我们使用逆散射方法解决该系统，以解决我们为解决WNT解决的混合时间边界条件。我们获得了描述示踪剂位置累积分布的样本到样本波动的较大偏差的速率函数。由于不对称性变化，它表现出跨界，从而恢复了MFT和KPZ极限。我们素描它如何与提取弗雷德姆决定因素公式的渐近学，该公式是最近用于粘稠的布朗尼运动的。这里研究的跨界机制应推广到MFT所描述的较大类别的模型。我们的结果适用于研究超出爱因斯坦理论的极端扩散。
We study the crossover from the macroscopic fluctuation theory (MFT) which describes 1D stochastic diffusive systems at late times, to the weak noise theory (WNT) which describes the Kardar-Parisi-Zhang (KPZ) equation at early times. We focus on the example of the diffusion in a time-dependent random field, observed in an atypical direction which induces an asymmetry. The crossover is described by a non-linear system which interpolates between the derivative and the standard non-linear Schrodinger equations in imaginary time. We solve this system using the inverse scattering method for mixed-time boundary conditions introduced by us to solve the WNT. We obtain the rate function which describes the large deviations of the sample-to-sample fluctuations of the cumulative distribution of the tracer position. It exhibits a crossover as the asymmetry is varied, recovering both MFT and KPZ limits. We sketch how it is consistent with extracting the asymptotics of a Fredholm determinant formula, recently derived for sticky Brownian motions. The crossover mechanism studied here should generalize to a larger class of models described by the MFT. Our results apply to study extremal diffusion beyond Einstein's theory.
