论文标题
对称排除过程的宏观波动理论的精确解
Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
论文作者
论文摘要
我们通过将规范的Cole-HOPF转换的概括与反向散射方法相结合，为对称简单排除过程的宏观波动理论（MFT）提供了第一个精确解。对于具有两个密度的步骤初始条件，可以解决相关的Riemann-Hilbert问题，以确定最佳密度曲线和响应场在初始和最后的时间都会产生所需的波动。电流的较大偏差函数是得出的，并与先前通过微观计算获得的公式重合。这提供了对在时间依赖性方案中MFT对相互作用模型的有效性的首次分析确认。
We present the first exact solution for the time dependent equations of the macroscopic fluctuation theory (MFT) for the symmetric simple exclusion process by combining a generalization of the canonical Cole-Hopf transformation with the inverse scattering method. For the step initial condition with two densities, the associated Riemann-Hilbert problem is solved to determine exactly the optimal density profile and the response field which produce a required fluctuation, both at initial and final times. The large deviation function of the current is derived and coincides with the formula obtained previously by microscopic calculations. This provides the first analytic confirmation of the validity of the MFT for an interacting model in the time dependent regime.
